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Manager  Joined: 23 Jan 2011
Posts: 98
The events A and B are independent, the probability that eve  [#permalink]

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1
16 00:00

Difficulty:   75% (hard)

Question Stats: 56% (02:36) correct 44% (02:45) wrong based on 232 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
Manager  Joined: 22 Oct 2013
Posts: 60
GMAT 1: 750 Q50 V42 Re: The events A and B are independent  [#permalink]

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10
6
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
##### General Discussion
Manager  Joined: 24 Apr 2013
Posts: 51
Location: United States
Re: The events A and B are independent  [#permalink]

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2
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 !!
_________________
Struggling: make or break attempt
Manager  Joined: 22 Oct 2013
Posts: 60
GMAT 1: 750 Q50 V42 Re: The events A and B are independent, the probability that eve  [#permalink]

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Thanks Chetan. Yes, I feel slightly less miserable in Maths than I do in Verbal:)
Non-Human User Joined: 09 Sep 2013
Posts: 13589
Re: The events A and B are independent, the probability that eve  [#permalink]

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_________________ Re: The events A and B are independent, the probability that eve   [#permalink] 15 Oct 2018, 10:27
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