GRE Prep 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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Retired Moderator
Joined: 19 Nov 2020
Posts: 326
Given Kudos: 64
GRE 1: Q160 V152
Events X and Y are independent.
[#permalink]
15 Aug 2021, 08:08
15 Aug 2021, 08:08
2
10
Bookmarks
00:00
Question Stats:
29% (01:54) correct
70% (01:00) wrong based on 61 sessions
Hide Show timer Statistics
Events X and Y are independent.
The probability that events X and Y both occur is 0.45
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Very hard
Source text edited/modified
The probability that events X and Y both occur is 0.45
Quantity A |
Quantity B |
The probability that event X occurs |
0.35 |
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Very hard
Source text edited/modified
Events X and Y are independent.
[#permalink]
23 Aug 2021, 13:05
23 Aug 2021, 13:05
2
Expert Reply
1
Bookmarks
If two events X and Y are independent, then the probability that both occur (P X AND Y) = P(X) . P(Y) and it is given that P(X) . P(Y) = 0.45
Here we know that the probability of an event 'E' is limited to the range 0 < P(E) < 1
The maximum probability that an event may occur is 1 and since we are trying to establish a lower bound for P(X), maximize P(Y) i.e. P(Y) = 1.
Given this situation:
P(X) x 1 = 0.45 \( \implies \) P(X) = 0.45.
Thus P(X) can never fall below this value and thus Qty A is greater.
Note: For the product of two quantities to result in a fixed value, to find the minimum possible value for one of the quantities, maximize the other.
Here we know that the probability of an event 'E' is limited to the range 0 < P(E) < 1
The maximum probability that an event may occur is 1 and since we are trying to establish a lower bound for P(X), maximize P(Y) i.e. P(Y) = 1.
Given this situation:
P(X) x 1 = 0.45 \( \implies \) P(X) = 0.45.
Thus P(X) can never fall below this value and thus Qty A is greater.
Re: Events X and Y are independent.
[#permalink]
15 Jun 2024, 10:43
15 Jun 2024, 10:43
Hello from the GRE Prep Club BumpBot!
Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
