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The events A and B are independent, the probability that eve

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Manager
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The events A and B are independent, the probability that eve  [#permalink]

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New post 22 Oct 2013, 07:30
1
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A
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56% (02:09) correct 44% (01:59) wrong based on 206 sessions

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The events A and B are independent, the probability that event A occurs is greater than 0, and the probability that event A occurs is twice the probability that event B occurs. The probability that at least one of events A and B occurs is 8 times the probability that both events A and B occur. What is the probability that event A occurs?

A. 1/12
B. 1/8
C. 1/6
D. 1/3
E. 2/3
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Manager
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Joined: 22 Oct 2013
Posts: 71
GMAT 1: 750 Q50 V42
Re: The events A and B are independent  [#permalink]

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New post 22 Oct 2013, 07:45
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The events A and B are independent, the probability that event A occurs is greater than 0, and the probability that event A occurs is twice the probability that event B occurs. The probability that at least one of events A and B occurs is 8 times the probability that both events A and B occur. What is the probability that event A occurs?

Let us say probability of A occuring is a.
Let us say probability of B occuring is b.

a = 2b

Probability (either A or B or both) = 8 times Probability (A and B)
a*(1-b) + b*(1-a) + ab = 8*ab

Substituting a=2b in the second equation:

2b*(1-b) + b*(1-2b) + 2b*b = 8*2b*b

3b-2b^2 = 16b^2
3b = 18b^2
b = 3/18 = 1/6

So, a = 2b = 1/3
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Manager
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Re: The events A and B are independent  [#permalink]

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New post 22 Oct 2013, 08:14
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ayushman wrote:
The events A and B are independent, the probability that event A occurs is greater than 0, and the probability that event A occurs is twice the probability that event B occurs. The probability that at least one of events A and B occurs is 8 times the probability that both events A and B occur. What is the probability that event A occurs?

Let us say probability of A occuring is a.
Let us say probability of B occuring is b.

a = 2b

Probability (either A or B or both) = 8 times Probability (A and B)
a*(1-b) + b*(1-a) + ab = 8*ab

Substituting a=2b in the second equation:

2b*(1-b) + b*(1-2b) + 2b*b = 8*2b*b

3b-2b^2 = 16b^2
3b = 18b^2
b = 3/18 = 1/6

So, a = 2b = 1/3



I see its your first day, welcome to the club :)
and already solving 700 level probability, way to go *thumbs up*
it took me 3 mins !!
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GMAT 1: 750 Q50 V42
Re: The events A and B are independent, the probability that eve  [#permalink]

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New post 22 Oct 2013, 09:35
Thanks Chetan. Yes, I feel slightly less miserable in Maths than I do in Verbal:)
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Re: The events A and B are independent, the probability that eve  [#permalink]

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New post 15 Oct 2018, 09:27
Hello from the GMAT Club BumpBot!

Thanks to another GMAT 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).

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Re: The events A and B are independent, the probability that eve &nbs [#permalink] 15 Oct 2018, 09:27
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