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Retired Moderator
Joined: 19 Nov 2020
Posts: 326
Given Kudos: 64
GRE 1: Q160 V152
Events X and Y are independent.
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15 Aug 2021, 08:08
15 Aug 2021, 08:08
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Question Stats:
34% (01:45) correct
65% (01:01) wrong based on 67 sessions
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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.
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23 Aug 2021, 13:05
23 Aug 2021, 13:05
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Expert Reply
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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.
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12 Oct 2025, 23:37
12 Oct 2025, 23:37
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