 It is currently 24 Nov 2020, 23:55 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # In a probability experiment, G and H are independent events  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS: Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 175

Kudos [?]: 3034  , given: 394

In a probability experiment, G and H are independent events [#permalink]
6
KUDOS
Expert's post 00:00

Question Stats: 31% (00:57) correct 68% (00:44) wrong based on 333 sessions
In a probability experiment, G and H are independent events. The probability that G will occur is r, and the probability that H will occur is s, where both r and s are greater than 0.

 Quantity A Quantity B The probability that either G will occur or H will occur, but not both r + s - rs

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Practice Questions
Question: 5
Page: 119
[Reveal] Spoiler: OA

_________________

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

Try our free Online GRE Test Manager Joined: 23 Jan 2016
Posts: 133
Followers: 4

Kudos [?]: 150  , given: 15

Re: In a probability experiment, G and H are independent events [#permalink]
2
KUDOS
A:
P(G union H) - P (G intersection H) = P(G) + P(H) - P (G intersection H) - P (G intersection H) = r + s -rs -rs = r + s -2rs

B:
r + s -rs

Clearly B is greater, hence the answer. Intern Joined: 22 Apr 2017
Posts: 1
Followers: 0

Kudos [?]: 16  , given: 0

Re: In a probability experiment, G and H are independent events [#permalink]
16
KUDOS
I struggled a bit with understanding the mathematics in this question, but I think I found a more intuitive way to explain the solution.

Attachment: Probability.png [ 4.17 KiB | Viewed 25654 times ]

Let the RED area equal r, or P(G), and let the BLUE area equal s, or P(H).

The PURPLE area, therefore, indicates the probability that G and H both occur, or P(G intersection H).

Since we're trying to find "The probability that either G will occur or H will occur, but not both," then we are trying to find the RED area and the BLUE area, but NOT the PURPLE area. To write this in probability terms, we would write P(G union H) - P (G intersection H) = P(G) - P (G intersection H) + P(H) - P (G intersection H)

The RED area is P(G)-P(G intersection H), or r-rs. The BLUE area is P(H)-P(G intersection H), or s-sr. You then simply add those too formulas together, resulting in r - rs + s - rs, which simplifies to r + s - 2rs. Intern Joined: 03 Dec 2017
Posts: 1
Followers: 0

Kudos [?]: 3  , given: 0

Re: In a probability experiment, G and H are independent events [#permalink]
3
KUDOS
For the official guide answer to be correct you have to assume G & H are not mutually exclusive events (events that can't both happen at the same time. If they were then R*S would equal 0 and A and B would be equal.

You have to be able to infer that since the probability of G happening doesn't effect the probability of H happening AND that r and s are greater than zero that G & H must not be mutually exclusive. Intern Joined: 12 Aug 2018
Posts: 9
Followers: 0

Kudos [?]: 4  , given: 3

Re: In a probability experiment, G and H are independent events [#permalink]
2
KUDOS
May I know why the formula P(G or H)= P(G)+P(H)-P(G&H) does not apply here. Thanks for the clarification. Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 175

Kudos [?]: 3034  , given: 394

Re: In a probability experiment, G and H are independent events [#permalink]
6
KUDOS
Expert's post
Runnyboy44 wrote:
May I know why the formula P(G or H)= P(G)+P(H)-P(G&H) does not apply here. Thanks for the clarification.

It is valid:

Probability that either event occurs = $$P(G)+P(H)-P(G&H)$$

Probability that either event occurs but not both = $$P(G)+P(H)-P(G&H)-P(G&H)= r+s-2rs$$. This is quantity A
_________________

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

Try our free Online GRE Test

Manager Joined: 22 Jul 2018
Posts: 80
Followers: 0

Kudos [?]: 15 , given: 42

Re: In a probability experiment, G and H are independent events [#permalink]
Here is one query(not related to above question), if the quantities are not mutually exclusive, then which formula should we use?

Formula for mutually exclusive P(A or B)= P(A) + P(B) Supreme Moderator
Joined: 01 Nov 2017
Posts: 371
Followers: 12

Kudos [?]: 186  , given: 4

Re: In a probability experiment, G and H are independent events [#permalink]
1
KUDOS
Expert's post
Sawant91 wrote:
Here is one query(not related to above question), if the quantities are not mutually exclusive, then which formula should we use?

Formula for mutually exclusive P(A or B)= P(A) + P(B)

HI,

Standard formula is P(A or B)= P(A) + P(B)-P(A and B)
Mutually exclusive means that the two events cannot happen at the same time, so intersection is 0, that is P(A ∩ B) = 0, so we are left with P(A or B)= P(A) + P(B)-P(A and B) = P(A) + P(B)-0 = P(A) + P(B)
_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html Manager Joined: 22 Feb 2018
Posts: 163
Followers: 2

Kudos [?]: 139  , given: 22

Re: In a probability experiment, G and H are independent events [#permalink]
2
KUDOS
G and H are independent events.
The probability that G will occur is r: P(G) = r > 0
The probability that H will occur is s: P(H) = s > 0
A: The probability that either G will occur or H will occur, but not both:
P(G delta H) = P(G and not H) + P(H and not G) = P(G)*P(H’) + P(H)*P(G’) = P(G)*(1- P(H)) + P(H)*(1- P(G)) = P(G) - P(G)*P(H) + P(H) -P(G)*P(H) =
P(G) + P(H) - 2P(H intersection G) = [since G and G are independent, P(H intersection G) equals probability of multiplication of them: P(G)*P(H)
= P(G) + P(H) - 2P(G)*P(H) = r + s - 2r*s

B= r + s - r*s
So B is bigger than A.
_________________ GRE Instructor Joined: 10 Apr 2015
Posts: 3907
Followers: 163

Kudos [?]: 4766  , given: 70

Re: In a probability experiment, G and H are independent events [#permalink]
2
KUDOS
Expert's post
sandy wrote:
In a probability experiment, G and H are independent events. The probability that G will occur is r, and the probability that H will occur is s, where both r and s are greater than 0.

 Quantity A Quantity B The probability that either G will occur or H will occur, but not both r + s - rs

Since G and H are independent events, we know that P(G and H) = rs
Also, since we're told that r and s are each greater than 0, we know that rs > 0
In other words, P(G and H) > 0

Now recognize that P(G or H) = P(G) + P(H) - P(G and H)
= r + s - rs
Aha! r + s - rs = P(G or H)
IMPORTANT: P(G or H) = P(G occurs, or H occurs or BOTH G and H occur)

So, we have:
QUANTITY A: P(G occurs, or H occurs not NOT BOTH G and H occur)
QUANTITY B: P(G occurs, or H occurs or BOTH G and H occur)

Since P(G and H) > 0, we can conclude that Quantity B is greater.

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com Manager Joined: 22 Aug 2019
Posts: 72
Followers: 1

Kudos [?]: 51 , given: 11

Re: In a probability experiment, G and H are independent events [#permalink]
sandy wrote:
In a probability experiment, G and H are independent events. The probability that G will occur is r, and the probability that H will occur is s, where both r and s are greater than 0.

 Quantity A Quantity B The probability that either G will occur or H will occur, but not both r + s - rs

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Practice Questions
Question: 5
Page: 119

A quick way of doing this is imagining a Venn diagram. Since these events are independent, we know that they must have some overlap (if they were mutually exclusive, there would be no overlap in our Venn diagram. By adding both A and B. We count the overlapping region twice. Thus RHS is how we could account for the probability of either event happening, but the LHS would no include that region.

So clearly B is larger than A.
Senior Manager Joined: 17 Aug 2019
Posts: 279
Followers: 2

Kudos [?]: 40 , given: 70

Re: In a probability experiment, G and H are independent events [#permalink]
GreenlightTestPrep wrote:
sandy wrote:
In a probability experiment, G and H are independent events. The probability that G will occur is r, and the probability that H will occur is s, where both r and s are greater than 0.

 Quantity A Quantity B The probability that either G will occur or H will occur, but not both r + s - rs

Since G and H are independent events, we know that P(G and H) = rs
Also, since we're told that r and s are each greater than 0, we know that rs > 0
In other words, P(G and H) > 0

Now recognize that P(G or H) = P(G) + P(H) - P(G and H)
= r + s - rs
Aha! r + s - rs = P(G or H)
IMPORTANT: P(G or H) = P(G occurs, or H occurs or BOTH G and H occur)

So, we have:
QUANTITY A: P(G occurs, or H occurs not NOT BOTH G and H occur)
QUANTITY B: P(G occurs, or H occurs or BOTH G and H occur)

Since P(G and H) > 0, we can conclude that Quantity B is greater.

Cheers,
Brent

I have a question:
Based on what you put,
Example :
A:
r= 1.5, s= 1.5, Both will happen =0
P( R or S )= 1.5+1.5 - 0 = 3

B;
Based on the previous, the value is 3. GRE Instructor Joined: 10 Apr 2015
Posts: 3907
Followers: 163

Kudos [?]: 4766  , given: 70

Re: In a probability experiment, G and H are independent events [#permalink]
1
KUDOS
Expert's post
Asmakan wrote:
I have a question:
Based on what you put,
Example :
A:
r= 1.5, s= 1.5, Both will happen =0
P( R or S )= 1.5+1.5 - 0 = 3

B;
Based on the previous, the value is 3.

There are a few issues with your question above.

First of all, the probability of an event is always less than or equal to one.
So, r and s cannot equal 1.5
Also, where does the zero come from in 1.5+1.5 - 0 = 3?
_________________

Brent Hanneson – Creator of greenlighttestprep.com Senior Manager Joined: 17 Aug 2019
Posts: 279
Followers: 2

Kudos [?]: 40 , given: 70

Re: In a probability experiment, G and H are independent events [#permalink]
GreenlightTestPrep wrote:
Asmakan wrote:
I have a question:
Based on what you put,
Example :
A:
r= 1.5, s= 1.5, Both will happen =0
P( R or S )= 1.5+1.5 - 0 = 3

B;
Based on the previous, the value is 3.

There are a few issues with your question above.

First of all, the probability of an event is always less than or equal to one.
So, r and s cannot equal 1.5
Also, where does the zero come from in 1.5+1.5 - 0 = 3?

Sorry, I was confused with another question.
Yes, I agree with u, probability can't be greater than 1.
In Q A, It is mentioned that the 2 probability don't happen with each other, " but not both ". So, the probability here is 0 Re: In a probability experiment, G and H are independent events   [#permalink] 15 Jun 2020, 01:40
Display posts from previous: Sort by

# In a probability experiment, G and H are independent events  Question banks Downloads My Bookmarks Reviews Important topics  Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.