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Events A and B are independent. The probability that events A and B bo

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Events A and B are independent. The probability that events A and B bo [#permalink] New post   21 Sep 2023, 10:22
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Events A and B are independent. The probability that events A and B both occur is 0.6


Quantity A
Quantity B
The probability that event A occurs
0.3



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



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A
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reno
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Re: Events A and B are independent. The probability that events A and B bo [#permalink] New post   22 Sep 2023, 01:30
How is the answer D?
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Re: Events A and B are independent. The probability that events A and B bo [#permalink] New post   22 Sep 2023, 01:37
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The answer is A. It is also under the spoiler
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Re: Events A and B are independent. The probability that events A and B bo [#permalink] New post   30 Sep 2023, 22:12
May someone please explain how to go about this question ?

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Re: Events A and B are independent. The probability that events A and B bo [#permalink] New post   30 Sep 2023, 22:58
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Having independent event we do have

\(P (A & B) = P (A) \times P (B)\)


Now we do know that the LHS is 0.6 as for the stem.

\(0.6= P (A) \times P (B)\)

Now we do also know that the probability is at most 1. We cannot have a probability >1

So we do have for example

A * B in the equation above and suppose that A is 0.3 B must be = 2 to have in the end both 0.6. And this is impossible.

Probability must be equal to 1 at most

IF both the result is 0.6 and B is 0.3 therefore A must be > 0.3 regardless any further calculations

A > B

See more on probability in our handout.

https://gre.myprepclub.com/forum/gre-pr ... tml#p83091
https://gre.myprepclub.com/forum/how-to ... ml#p100949
https://gre.myprepclub.com/forum/how-to ... ml#p100952
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