It is currently 14 Jun 2021, 01:32 |

Customized

for You

Track

Your Progress

Practice

Pays

- Jun
**14**### Free Workshop for the GRE

08:00 PM EDT

-09:30 PM EDT

There is no mystery to scoring high on the GRE. It is prep. Start with this free, teacher-led GRE Workshop. You will review key content, and pick up strategies to help you answer questions faster. - Jun
**11**### 10% off & 3 free months

09:00 AM EDT

-11:59 PM EDT

The Economist GRE Tutor are offering 10% off and 3 additional months added to their 6-month Genius plan if you purchase with the promo code GENIUS9. With included private tutoring sessions, official ETS practice exams, and more. Offer ends Mon, June 14th - Jun
**17**### Greenlight Test Prep Free Content

08:00 PM EDT

-09:00 PM EDT

Free Video Modules Within each of the 16 learning modules (Geometry, Statistics, Sentence Equivalence, etc.) that comprise the course, you'll find plenty of free videos to help you make an informed purchase. - Jun
**24**### Is a GMAT or GRE Tutor Worth It?

08:00 PM PDT

-10:00 PM PDT

In this article, we’ll explore how much a GMAT tutor costs relative to other options. Then we’ll discuss why you might hire a GMAT tutor as your preferred GMAT prep option. - Jun
**26**### Free GRE Practice Tests with Magoosh

06:00 PM PDT

-11:00 PM PDT

Test prep can be expensive—but it doesn’t have to be! One of the best tools in your GRE prep toolkit is a quality practice exam. And you can definitely find a free GRE practice test online, if you know where to look!

QOTD # 19 For a certain probability experiment, the probabil
[#permalink]
12 Sep 2016, 02:02

3

Expert Reply

8

Bookmarks

Question Stats:

For a certain probability experiment, the probability that event A will occur is \(\frac{1}{2}\) and the probability that event B will occur is \(\frac{1}{3}\). Which of the following values could be the probability that the event A ∪ B (that is, the event A or B, or both) will occur?

Indicate all such values.

_________________

Indicate all such values.

- A) \(\frac{1}{3}\)

B) \(\frac{1}{2}\)

C) \(\frac{3}{4}\)

Practice Questions

Question: 19

Page: 181

Question: 19

Page: 181

_________________

GRE Prep Club OFFICIAL Android App

New to the GRE, and GRE CLUB Forum?

GRE: All you do need to know about the GRE Test | GRE Prep Club for the GRE Exam - The Complete FAQ

Search GRE Specific Questions | Download Vault

Posting Rules: QUANTITATIVE | VERBAL

FREE Resources: GRE Prep Club Official LinkTree Page | Free GRE Materials - Where to get it!! (2020)

Free GRE Prep Club Tests: Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club on : Facebook | Instagram

Questions' Banks and Collection:

ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides

3rd Party Resource's: All Quant Questions Collection | All Verbal Questions Collection

Books: All GRE Best Books

Scores: The GRE average score at Top 25 Business Schools 2020 Ed. | How to study for GRE retake and score HIGHER - (2020)

How is the GRE Score Calculated -The Definitive Guide (2021)

Tests: GRE Prep Club Tests | FREE GRE Practice Tests [Collection] - New Edition (2021)

Vocab: GRE Prep Club Official Vocabulary Lists for the GRE (2021)

New to the GRE, and GRE CLUB Forum?

GRE: All you do need to know about the GRE Test | GRE Prep Club for the GRE Exam - The Complete FAQ

Search GRE Specific Questions | Download Vault

Posting Rules: QUANTITATIVE | VERBAL

FREE Resources: GRE Prep Club Official LinkTree Page | Free GRE Materials - Where to get it!! (2020)

Free GRE Prep Club Tests: Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club on : Facebook | Instagram

Questions' Banks and Collection:

ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides

3rd Party Resource's: All Quant Questions Collection | All Verbal Questions Collection

Books: All GRE Best Books

Scores: The GRE average score at Top 25 Business Schools 2020 Ed. | How to study for GRE retake and score HIGHER - (2020)

How is the GRE Score Calculated -The Definitive Guide (2021)

Tests: GRE Prep Club Tests | FREE GRE Practice Tests [Collection] - New Edition (2021)

Vocab: GRE Prep Club Official Vocabulary Lists for the GRE (2021)

Re: QOTD # 19 For a certain probability experiment, the probabil
[#permalink]
12 Sep 2016, 02:10

7

Expert Reply

1

Bookmarks

Explanation

Since you know that the probability of event A is \(\frac{1}{2}\)and the probability of event B is \(\frac{1}{3}\) but you are not given any information about the relationship between events A and B, you can compute only the minimum possible value and the maximum possible value of the probability of the event A ∪ B. The probability of A ∪ B is least if B is a subset of A; in that case, the probability of A ∪ B is just the probability of A, or \(\frac{1}{2}\) .

The probability of A ∪ B is greatest if A and B do not intersect at all; in that case, the probability of A ∪ B is the sum of the probabilities of A and B, or \(\frac{1}{2} + \frac{1}{3} = \frac{5}{6}\) With no further information about A and B, the probability that A or B, or both, will occur could be any number from \(\frac{1}{2}\) to \(\frac{5}{6}\).

Of the answer choices given, only \(\frac{1}{2}\) and \(\frac{3}{4}\) are in this interval.

The correct answer consists of Choices B and C.

_________________

GRE Prep Club OFFICIAL Android App

New to the GRE, and GRE CLUB Forum?

GRE: All you do need to know about the GRE Test | GRE Prep Club for the GRE Exam - The Complete FAQ

Search GRE Specific Questions | Download Vault

Posting Rules: QUANTITATIVE | VERBAL

FREE Resources: GRE Prep Club Official LinkTree Page | Free GRE Materials - Where to get it!! (2020)

Free GRE Prep Club Tests: Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club on : Facebook | Instagram

Questions' Banks and Collection:

ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides

3rd Party Resource's: All Quant Questions Collection | All Verbal Questions Collection

Books: All GRE Best Books

Scores: The GRE average score at Top 25 Business Schools 2020 Ed. | How to study for GRE retake and score HIGHER - (2020)

How is the GRE Score Calculated -The Definitive Guide (2021)

Tests: GRE Prep Club Tests | FREE GRE Practice Tests [Collection] - New Edition (2021)

Vocab: GRE Prep Club Official Vocabulary Lists for the GRE (2021)

Since you know that the probability of event A is \(\frac{1}{2}\)and the probability of event B is \(\frac{1}{3}\) but you are not given any information about the relationship between events A and B, you can compute only the minimum possible value and the maximum possible value of the probability of the event A ∪ B. The probability of A ∪ B is least if B is a subset of A; in that case, the probability of A ∪ B is just the probability of A, or \(\frac{1}{2}\) .

The probability of A ∪ B is greatest if A and B do not intersect at all; in that case, the probability of A ∪ B is the sum of the probabilities of A and B, or \(\frac{1}{2} + \frac{1}{3} = \frac{5}{6}\) With no further information about A and B, the probability that A or B, or both, will occur could be any number from \(\frac{1}{2}\) to \(\frac{5}{6}\).

Of the answer choices given, only \(\frac{1}{2}\) and \(\frac{3}{4}\) are in this interval.

The correct answer consists of Choices B and C.

_________________

New to the GRE, and GRE CLUB Forum?

GRE: All you do need to know about the GRE Test | GRE Prep Club for the GRE Exam - The Complete FAQ

Search GRE Specific Questions | Download Vault

Posting Rules: QUANTITATIVE | VERBAL

FREE Resources: GRE Prep Club Official LinkTree Page | Free GRE Materials - Where to get it!! (2020)

Free GRE Prep Club Tests: Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club on : Facebook | Instagram

Questions' Banks and Collection:

ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides

3rd Party Resource's: All Quant Questions Collection | All Verbal Questions Collection

Books: All GRE Best Books

Scores: The GRE average score at Top 25 Business Schools 2020 Ed. | How to study for GRE retake and score HIGHER - (2020)

How is the GRE Score Calculated -The Definitive Guide (2021)

Tests: GRE Prep Club Tests | FREE GRE Practice Tests [Collection] - New Edition (2021)

Vocab: GRE Prep Club Official Vocabulary Lists for the GRE (2021)

Re: QOTD # 19 For a certain probability experiment, the probabil
[#permalink]
03 May 2018, 20:59

5

novice07 wrote:

I agree with the official explanation, but there was a similar question https://greprepclub.com/forum/probabili ... -8733.html wherein we had a discussion about the minimum probability of the events.

Why is the option 1st also not correct? Since the event B can occur with 1/3 probability

Why is the option 1st also not correct? Since the event B can occur with 1/3 probability

Probability of event \(B\) is \(0.5\)

Probability of event \(A\) is \(0.3333\)

Given that probability of event \(B\) is greater than \(A\)

one A U B scenario could involve event \(A\) being a subset of \(B\) hence minimum possible union will be \(0.5\)

However if the two probabilities are mutually exclusive \(A + B\) would be \(0.8333\) which would be the maximum probability

as such the range of probability for A U B is \(0.5\) to \(0.8333\) inclusive

_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos

Re: QOTD # 19 For a certain probability experiment, the probabil
[#permalink]
11 Feb 2018, 19:13

1

Dear Carcass, please could you help me…

Since we don’t know the relationship between A and B my assumption is based on the following

Two extreme cases:

1. If the events A and B are not mutually exclusive, then p(A or B) = p(A) + p(B) - p(A and B).

p(A or B) = ½+1/3-1/6=2/3

2. If events A and B are mutually exclusive, then the probability of A or B is simply:

p(A or B) = p(A) + p(B).

p(A or B) = ½+1/3=5/6

Thus, I assumed correct answer should be just C

Since we don’t know the relationship between A and B my assumption is based on the following

Two extreme cases:

1. If the events A and B are not mutually exclusive, then p(A or B) = p(A) + p(B) - p(A and B).

p(A or B) = ½+1/3-1/6=2/3

2. If events A and B are mutually exclusive, then the probability of A or B is simply:

p(A or B) = p(A) + p(B).

p(A or B) = ½+1/3=5/6

Thus, I assumed correct answer should be just C

Retired Moderator

Joined: **07 Jun 2014 **

Posts: **4804**

WE:**Business Development (Energy and Utilities)**

Re: QOTD # 19 For a certain probability experiment, the probabil
[#permalink]
12 Feb 2018, 04:07

2

Expert Reply

This is the correct expression

P(A ∪ B) = P(A) + P(B) - P(B)P( A | B )

P(A) is probability of A happening

P(B) is probability of B happening

P( B | A ) can be said to Probability of B given that A has occured. Now look at the figure below. The area P( A | B ) is minimum when P(A) and P(B) do not overlap at all.

Inkedgeom121211_LI.jpg [ 835.65 KiB | Viewed 31332 times ]

.

Intutive explanation of the formula:

P(A ∪ B) = P(A) + P(B) - P(B)P( A | B )

If you look at the figure to find area of P(A ∪ B) we add the area of P(A) and P(B) but if P(A) and P(B) overlap, we would add the overlapping area twice! So we sunbtract P(B)P( A | B ).

Example:

An urn contains 6 red marbles and 4 black marbles. Two marbles are drawn without replacement from the urn. What is the probability that both of the marbles are black?

Let A = the event that the first marble is black; and let B = the event that the second marble is black.

We know the following:

In the beginning, there are 10 marbles in the urn, 4 of which are black. Therefore, P(A) = 4/10.

After the first selection, there are 9 marbles in the urn, 3 of which are black. Therefore, P(B|A) = 3/9.

P(A) P(B|A) = (4/10) * (3/9) = 12/90 = 2/15 = 0.133

P(B)P( A | B ) is not P(B)P(A). The amount of overlapping area cannot be found out unless specified

Please take care of this as this is the very fundamental concept of probability. Hope this helps and feel free to ask more questions.

_________________

P(A ∪ B) = P(A) + P(B) - P(B)P( A | B )

P(A) is probability of A happening

P(B) is probability of B happening

P( B | A ) can be said to Probability of B given that A has occured. Now look at the figure below. The area P( A | B ) is minimum when P(A) and P(B) do not overlap at all.

Attachment:

Inkedgeom121211_LI.jpg [ 835.65 KiB | Viewed 31332 times ]

Intutive explanation of the formula:

P(A ∪ B) = P(A) + P(B) - P(B)P( A | B )

If you look at the figure to find area of P(A ∪ B) we add the area of P(A) and P(B) but if P(A) and P(B) overlap, we would add the overlapping area twice! So we sunbtract P(B)P( A | B ).

Example:

An urn contains 6 red marbles and 4 black marbles. Two marbles are drawn without replacement from the urn. What is the probability that both of the marbles are black?

Let A = the event that the first marble is black; and let B = the event that the second marble is black.

We know the following:

In the beginning, there are 10 marbles in the urn, 4 of which are black. Therefore, P(A) = 4/10.

After the first selection, there are 9 marbles in the urn, 3 of which are black. Therefore, P(B|A) = 3/9.

P(A) P(B|A) = (4/10) * (3/9) = 12/90 = 2/15 = 0.133

P(B)P( A | B ) is not P(B)P(A). The amount of overlapping area cannot be found out unless specified

Please take care of this as this is the very fundamental concept of probability. Hope this helps and feel free to ask more questions.

_________________

Sandy

If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Re: QOTD # 19 For a certain probability experiment, the probabil
[#permalink]
07 Apr 2018, 07:36

It is a confusing question.

The probability of event A occurring without event B occurring is P(A) * (1-P(B) = 1/2 * (1-1/3) = 2/6

The probability of event B occurring without event A occurring is P(B) * (1-P(A) = 1/3 * (1-1/2) = 1/6

The probability of both event A & B occurring is P(A) * P(B) = 1/2 * 1/3 = 1/6

Thus, The probability of event A ∪ B (that is, the event A or B, or both) occurring is the sum of the above 2/6+1/6+1/6 = 5/6.

No answer is given!

The probability of event A occurring without event B occurring is P(A) * (1-P(B) = 1/2 * (1-1/3) = 2/6

The probability of event B occurring without event A occurring is P(B) * (1-P(A) = 1/3 * (1-1/2) = 1/6

The probability of both event A & B occurring is P(A) * P(B) = 1/2 * 1/3 = 1/6

Thus, The probability of event A ∪ B (that is, the event A or B, or both) occurring is the sum of the above 2/6+1/6+1/6 = 5/6.

No answer is given!

Re: QOTD # 19 For a certain probability experiment, the probabil
[#permalink]
07 Apr 2018, 07:53

Expert Reply

The answers are B and C.

It is an official question.

Regards

_________________

GRE Prep Club OFFICIAL Android App

New to the GRE, and GRE CLUB Forum?

GRE: All you do need to know about the GRE Test | GRE Prep Club for the GRE Exam - The Complete FAQ

Search GRE Specific Questions | Download Vault

Posting Rules: QUANTITATIVE | VERBAL

FREE Resources: GRE Prep Club Official LinkTree Page | Free GRE Materials - Where to get it!! (2020)

Free GRE Prep Club Tests: Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club on : Facebook | Instagram

Questions' Banks and Collection:

ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides

3rd Party Resource's: All Quant Questions Collection | All Verbal Questions Collection

Books: All GRE Best Books

Scores: The GRE average score at Top 25 Business Schools 2020 Ed. | How to study for GRE retake and score HIGHER - (2020)

How is the GRE Score Calculated -The Definitive Guide (2021)

Tests: GRE Prep Club Tests | FREE GRE Practice Tests [Collection] - New Edition (2021)

Vocab: GRE Prep Club Official Vocabulary Lists for the GRE (2021)

It is an official question.

Regards

_________________

New to the GRE, and GRE CLUB Forum?

GRE: All you do need to know about the GRE Test | GRE Prep Club for the GRE Exam - The Complete FAQ

Search GRE Specific Questions | Download Vault

Posting Rules: QUANTITATIVE | VERBAL

FREE Resources: GRE Prep Club Official LinkTree Page | Free GRE Materials - Where to get it!! (2020)

Free GRE Prep Club Tests: Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club on : Facebook | Instagram

Questions' Banks and Collection:

ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides

3rd Party Resource's: All Quant Questions Collection | All Verbal Questions Collection

Books: All GRE Best Books

Scores: The GRE average score at Top 25 Business Schools 2020 Ed. | How to study for GRE retake and score HIGHER - (2020)

How is the GRE Score Calculated -The Definitive Guide (2021)

Tests: GRE Prep Club Tests | FREE GRE Practice Tests [Collection] - New Edition (2021)

Vocab: GRE Prep Club Official Vocabulary Lists for the GRE (2021)

Re: QOTD # 19 For a certain probability experiment, the probabil
[#permalink]
10 Apr 2018, 01:33

I agree with the official explanation, but there was a similar question https://greprepclub.com/forum/probabili ... -8733.html wherein we had a discussion about the minimum probability of the events.

Why is the option 1st also not correct? Since the event B can occur with 1/3 probability

Why is the option 1st also not correct? Since the event B can occur with 1/3 probability

Re: QOTD # 19 For a certain probability experiment, the probabil
[#permalink]
17 Sep 2018, 09:59

Carcass wrote:

Explanation

Since you know that the probability of event A is \(\frac{1}{2}\)and the probability of event B is \(\frac{1}{3}\) but you are not given any information about the relationship between events A and B, you can compute only the minimum possible value and the maximum possible value of the probability of the event A ∪ B. The probability of A ∪ B is least if B is a subset of A; in that case, the probability of A ∪ B is just the probability of A, or \(\frac{1}{2}\) .

The probability of A ∪ B is greatest if A and B do not intersect at all; in that case, the probability of A ∪ B is the sum of the probabilities of A and B, or \(\frac{1}{2} + \frac{1}{3} = \frac{5}{6}\) With no further information about A and B, the probability that A or B, or both, will occur could be any number from \(\frac{1}{2}\) to \(\frac{5}{6}\).

Of the answer choices given, only \(\frac{1}{2}\) and \(\frac{3}{4}\) are in this interval.

The correct answer consists of Choices B and C.

Since you know that the probability of event A is \(\frac{1}{2}\)and the probability of event B is \(\frac{1}{3}\) but you are not given any information about the relationship between events A and B, you can compute only the minimum possible value and the maximum possible value of the probability of the event A ∪ B. The probability of A ∪ B is least if B is a subset of A; in that case, the probability of A ∪ B is just the probability of A, or \(\frac{1}{2}\) .

The probability of A ∪ B is greatest if A and B do not intersect at all; in that case, the probability of A ∪ B is the sum of the probabilities of A and B, or \(\frac{1}{2} + \frac{1}{3} = \frac{5}{6}\) With no further information about A and B, the probability that A or B, or both, will occur could be any number from \(\frac{1}{2}\) to \(\frac{5}{6}\).

Of the answer choices given, only \(\frac{1}{2}\) and \(\frac{3}{4}\) are in this interval.

The correct answer consists of Choices B and C.

Event B has more terms than event A, shouldn't A be a subset of B, which gives minimum probability as 1/3?

Re: QOTD # 19 For a certain probability experiment, the probabil
[#permalink]
13 Jun 2019, 06:08

6

Expert Reply

Carcass wrote:

For a certain probability experiment, the probability that event A will occur is \(\frac{1}{2}\) and the probability that event B will occur is \(\frac{1}{3}\). Which of the following values could be the probability that the event A ∪ B (that is, the event A or B, or both) will occur?

Indicate all such values.

Indicate all such values.

- A) \(\frac{1}{3}\)

B) \(\frac{1}{2}\)

C) \(\frac{3}{4}\)

-----------ASIDE-----------------

Key Concept #1: P(J OR K) = P(J) + P(K) - P(J and K)

Key Concept #2: P(J and K) ≤ P(J) & P(J and K) ≤ P(K)

This should make sense.

For example, P(it rains AND it snows tomorrow) must be less than or equal to P(it rains tomorrow)

---------------------------------

GIVEN:

P(A) = 1/2

P(B) = 1/3

From Key Concept #2 above, we know that P(A and B) ≤ 1/2, and we know that P(A and B) ≤ 1/3

So, the greatest possible value of P(A and B) is 1/3...

And the least possible value of P(A and B) is 0

We want to calculate P(A OR B)

P(A OR B) = P(A) + P(B) - P(A and B)

= 1/2 + 1/3 - P(A and B)

If P(A and B) = 1/3, then P(A OR B) = 1/2 + 1/3 - 1/3 = 1/2

If P(A and B) = 0, then P(A OR B) = 1/2 + 1/3 - 0 = 5/6

So, the RANGE of possible values of P(A OR B) goes from 1/2 to 5/6 (inclusive)

Check the answer choices....B and C are within the range of 1/2 to 5/6 (inclusive)

Answer: B & C

Cheers,

Brent

_________________

Re: QOTD # 19 For a certain probability experiment, the probabil
[#permalink]
17 Aug 2019, 01:51

GreenlightTestPrep wrote:

Carcass wrote:

For a certain probability experiment, the probability that event A will occur is \(\frac{1}{2}\) and the probability that event B will occur is \(\frac{1}{3}\). Which of the following values could be the probability that the event A ∪ B (that is, the event A or B, or both) will occur?

Indicate all such values.

Indicate all such values.

- A) \(\frac{1}{3}\)

B) \(\frac{1}{2}\)

C) \(\frac{3}{4}\)

-----------ASIDE-----------------

Key Concept #1: P(J OR K) = P(J) + P(K) - P(J and K)

Key Concept #2: P(J and K) ≤ P(J) & P(J and K) ≤ P(K)

This should make sense.

For example, P(it rains AND it snows tomorrow) must be less than or equal to P(it rains tomorrow)

---------------------------------

GIVEN:

P(A) = 1/2

P(B) = 1/3

From Key Concept #2 above, we know that P(A and B) ≤ 1/2, and we know that P(A and B) ≤ 1/3

So, the greatest possible value of P(A and B) is 1/3...

And the least possible value of P(A and B) is 0

We want to calculate P(A OR B)

P(A OR B) = P(A) + P(B) - P(A and B)

= 1/2 + 1/3 - P(A and B)

If P(A and B) = 1/3, then P(A OR B) = 1/2 + 1/3 - 1/3 = 1/2

If P(A and B) = 0, then P(A OR B) = 1/2 + 1/3 - 0 = 5/6

So, the RANGE of possible values of P(A OR B) goes from 1/2 to 5/6 (inclusive)

Check the answer choices....B and C are within the range of 1/2 to 5/6 (inclusive)

Answer: B & C

Cheers,

Brent

-------> For a certain probability experiment, the probability that event A will occur is 1/2 and the probability that event B will occur is 1/3. Which of the following values could be the probability that the event A ∪ B (that is, the event A or B, or both) will occur?

THIS IS CONFUSING! SOMEONE HELP ME PLEASE

Re: QOTD # 19 For a certain probability experiment, the probabil
[#permalink]
17 Aug 2019, 05:54

1

Expert Reply

anamx wrote:

-------> For a certain probability experiment, the probability that event A will occur is 1/2 and the probability that event B will occur is 1/3. Which of the following values could be the probability that the event A ∪ B (that is, the event A or B, or both) will occur?

THIS IS CONFUSING! SOMEONE HELP ME PLEASE

Don't worry about the "A ∪ B" notation. You aren't expected to know it on test day.

On test day, the question will as us to find P(A or B).

Also note that this is a VERY tricky question (to date, only 33% of students have correctly answered the question.

Cheers,

Brent

_________________

Re: QOTD # 19 For a certain probability experiment, the probabil
[#permalink]
06 Sep 2019, 03:20

Carcass wrote:

For a certain probability experiment, the probability that event A will occur is \(\frac{1}{2}\) and the probability that event B will occur is \(\frac{1}{3}\). Which of the following values could be the probability that the event A ∪ B (that is, the event A or B, or both) will occur?

Indicate all such values.

Indicate all such values.

- A) \(\frac{1}{3}\)

B) \(\frac{1}{2}\)

C) \(\frac{3}{4}\)

Practice Questions

Question: 19

Page: 181

Question: 19

Page: 181

Since we get 2/3 and 5/6, each equals 0.66 and 0.83 respectively, hence only option C comes between these 2 integers.

Re: QOTD # 19 For a certain probability experiment, the probabil
[#permalink]
03 Nov 2019, 06:27

1

mdishan95 wrote:

Carcass wrote:

For a certain probability experiment, the probability that event A will occur is \(\frac{1}{2}\) and the probability that event B will occur is \(\frac{1}{3}\). Which of the following values could be the probability that the event A ∪ B (that is, the event A or B, or both) will occur?

Indicate all such values.

Indicate all such values.

- A) \(\frac{1}{3}\)

B) \(\frac{1}{2}\)

C) \(\frac{3}{4}\)

Practice Questions

Question: 19

Page: 181

Question: 19

Page: 181

Since we get 2/3 and 5/6, each equals 0.66 and 0.83 respectively, hence only option C comes between these 2 integers.

How you got \(\frac{2}{3}\)?

_________________

If you found this post useful, please let me know by pressing the Kudos Button

Rules for Posting

Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club Members of the Month:TOP 10 members of the month with highest kudos receive access to 3 months GRE Prep Club tests

Rules for Posting

Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club Members of the Month:TOP 10 members of the month with highest kudos receive access to 3 months GRE Prep Club tests

Moderator

Joined: **16 Apr 2020 **

Status:**Founder & Quant Expert**

Affiliations: **Prepster Education**

Posts: **929**

Location: **India**

WE:**Education (Education)**

QOTD # 19 For a certain probability experiment, the probabil
[#permalink]
22 Feb 2021, 01:58

Carcass wrote:

For a certain probability experiment, the probability that event A will occur is \(\frac{1}{2}\) and the probability that event B will occur is \(\frac{1}{3}\). Which of the following values could be the probability that the event A ∪ B (that is, the event A or B, or both) will occur?

Indicate all such values.

Indicate all such values.

- A) \(\frac{1}{3}\)

B) \(\frac{1}{2}\)

C) \(\frac{3}{4}\)

Practice Questions

Question: 19

Page: 181

Question: 19

Page: 181

Prob. (A will occur) = \(\frac{1}{2}\)

Prob. (A will not occur) = \(1 - (\frac{1}{2}) = \frac{1}{2}\)

Prob. (B will occur) = \(\frac{1}{3}\)

Prob. (B will not occur) = \(1 - (\frac{1}{3}) = \frac{2}{3}\)

1. Prob. (only A will occur) = P (A will occur) x P (B will not occur) = \((\frac{1}{2})(\frac{2}{3}) = \frac{1}{3}\)

2. Prob. (only B will occur) = P (B will occur) x P (A will not occur) = \((\frac{1}{3})(\frac{1}{2}) = \frac{1}{6}\)

3. Prob. (both A and B will occur) = P (A will occur) x P (B will occur) = \((\frac{1}{2})(\frac{1}{3}) = \frac{1}{6}\)

4. Prob. (either A or B will occur) = P (A will occur) x P (B will not occur) + P (B will occur) x P (A will not occur) = \((\frac{1}{3}) + (\frac{1}{6}) = \frac{1}{2}\)

Only 2 option match our cases.

Hence, option B and C

_________________

I hope this helps!

Regards:

Karun Mendiratta

Founder and Quant Expert

Prepster Education

http://www.prepster.in

https://www.facebook.com/prepstereducation

Regards:

Karun Mendiratta

Founder and Quant Expert

Prepster Education

http://www.prepster.in

https://www.facebook.com/prepstereducation

gmatclubot

Moderators:

Multiple-choice Questions — Select One or More Answer Choices |
||

## Hi Guest,Here are updates for you:## GRE Prep Club REWARDS |