May 26 10:00 PM PDT  11:00 PM PDT Take 20% off the plan of your choice, now through midnight on May 26th Promo code MAGOOSH20SALE May 27 10:30 AM EDT  11:30 AM EDT Learn about the pros and cons of the two primary business school admissions exams from an applicant perspective. May 27 08:00 PM PDT  09:00 PM PDT Interact for GRE is an adaptive, interactive learning experience made by top 1% GRE pros. Available anytime, anywhere. Jun 01 08:00 PM PDT  09:00 PM PDT With Kaplan take a free practice test, attend a sample class with one of our highestrated teachers, or challenge yourself with a GRE bootcamp. Jun 02 10:00 PM PDT  11:00 PM PDT Target Test Prep GRE A REVOLUTIONARY ONDEMAND GRE PREP COURSE
Author 
Message 
TAGS:


Founder
Joined: 18 Apr 2015
Posts: 11096
Followers: 237
Kudos [?]:
2769
[2]
, given: 10521

QOTD # 19 For a certain probability experiment, the probabil [#permalink]
12 Sep 2016, 02:02
2
This post received KUDOS
Question Stats:
38% (00:54) correct
61% (01:24) wrong based on 103 sessions
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. A) \(\frac{1}{3}\)
B) \(\frac{1}{2}\)
C) \(\frac{3}{4}\) Practice Questions Question: 19 Page: 181
_________________
Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.




Founder
Joined: 18 Apr 2015
Posts: 11096
Followers: 237
Kudos [?]:
2769
[4]
, given: 10521

Re: QOTD # 19 For a certain probability experiment, the probabil [#permalink]
12 Sep 2016, 02:10
4
This post received KUDOS
ExplanationSince 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.
_________________
Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.



Intern
Joined: 20 Dec 2017
Posts: 30
Followers: 0
Kudos [?]:
18
[1]
, given: 9

Re: QOTD # 19 For a certain probability experiment, the probabil [#permalink]
11 Feb 2018, 19:13
1
This post received KUDOS
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+1/31/6=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: 4806
WE: Business Development (Energy and Utilities)
Followers: 162
Kudos [?]:
2654
[2]
, given: 394

Re: QOTD # 19 For a certain probability experiment, the probabil [#permalink]
12 Feb 2018, 04:07
2
This post received KUDOS
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. Attachment:
Inkedgeom121211_LI.jpg [ 835.65 KiB  Viewed 19922 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(BA) = 3/9. P(A) P(BA) = (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



Intern
Joined: 15 Mar 2018
Posts: 32
Followers: 0
Kudos [?]:
9
[0], given: 1

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) * (1P(B) = 1/2 * (11/3) = 2/6 The probability of event B occurring without event A occurring is P(B) * (1P(A) = 1/3 * (11/2) = 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!



Founder
Joined: 18 Apr 2015
Posts: 11096
Followers: 237
Kudos [?]:
2769
[0], given: 10521

Re: QOTD # 19 For a certain probability experiment, the probabil [#permalink]
07 Apr 2018, 07:53
The answers are B and C. It is an official question. Regards
_________________
Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.



Intern
Joined: 20 Mar 2018
Posts: 39
GRE 1: Q163 V149 GRE 2: Q168 V162
GPA: 3.5
Followers: 1
Kudos [?]:
39
[0], given: 8

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



Director
Joined: 07 Jan 2018
Posts: 694
Followers: 11
Kudos [?]:
741
[4]
, given: 88

Re: QOTD # 19 For a certain probability experiment, the probabil [#permalink]
03 May 2018, 20:59
4
This post received KUDOS
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 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
_________________
This is my response to the question and may be incorrect. Feel free to rectify any mistakes Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos



Manager
Joined: 27 Feb 2017
Posts: 188
Followers: 1
Kudos [?]:
72
[0], given: 15

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



GRE Instructor
Joined: 10 Apr 2015
Posts: 3244
Followers: 124
Kudos [?]:
3619
[3]
, given: 61

Re: QOTD # 19 For a certain probability experiment, the probabil [#permalink]
13 Jun 2019, 06:08
3
This post received KUDOS
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. 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) = 1/2P(B) = 1/3From Key Concept #2 above, we know that P(A and B) ≤ 1/2, and we know that P(A and B) ≤ 1/3So, the greatest possible value of P(A and B) is 1/3... And the least possible value of P(A and B) is 0We 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
_________________
Brent Hanneson – Creator of greenlighttestprep.com Sign up for my free GRE Question of the Day emails



Intern
Joined: 15 Jul 2019
Posts: 1
Followers: 0
Kudos [?]:
0
[0], given: 1

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. 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) = 1/2P(B) = 1/3From Key Concept #2 above, we know that P(A and B) ≤ 1/2, and we know that P(A and B) ≤ 1/3So, the greatest possible value of P(A and B) is 1/3... And the least possible value of P(A and B) is 0We 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



GRE Instructor
Joined: 10 Apr 2015
Posts: 3244
Followers: 124
Kudos [?]:
3619
[1]
, given: 61

Re: QOTD # 19 For a certain probability experiment, the probabil [#permalink]
17 Aug 2019, 05:54
1
This post received KUDOS
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
_________________
Brent Hanneson – Creator of greenlighttestprep.com Sign up for my free GRE Question of the Day emails



Intern
Joined: 23 Mar 2019
Posts: 27
Location: India
Followers: 0
Kudos [?]:
17
[0], given: 1

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. A) \(\frac{1}{3}\)
B) \(\frac{1}{2}\)
C) \(\frac{3}{4}\) Practice Questions 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.



VP
Joined: 20 Apr 2016
Posts: 1278
WE: Engineering (Energy and Utilities)
Followers: 19
Kudos [?]:
1199
[1]
, given: 241

Re: QOTD # 19 For a certain probability experiment, the probabil [#permalink]
03 Nov 2019, 06:27
1
This post received KUDOS
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. A) \(\frac{1}{3}\)
B) \(\frac{1}{2}\)
C) \(\frac{3}{4}\) Practice Questions 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




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





