Probability

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Abdulla
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Topic: Probability
PostWed Jul 01, 2009 4:22 pm Reply with quote
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

OA is D
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tohellandback
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PostWed Jul 01, 2009 6:28 pm Reply with quote
D
let prob B=x
prob A=2x
from the condition given
atleast A or B:
A not B
B not A
Both
x(1-2x)+x*2x+2x(1-x)=8*x*2x
it gives x=1/6
2x=1/3 answer
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cata1yst
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PostThu Jul 02, 2009 9:46 am Reply with quote
tohellandback wrote:
D
let prob B=x
prob A=2x
from the condition given
atleast A or B:
A not B
B not A
Both
x(1-2x)+x*2x+2x(1-x)=8*x*2x
it gives x=1/6
2x=1/3 answer
Please explain furthur how you get this equation...
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tohellandback
GMAT Destroyer!



Joined: 17 May 2009
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PostThu Jul 02, 2009 6:13 pm Reply with quote
Abdulla 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?


(A)1/12
(B)1/8
(C)1/6
(D)1/3
(E)2/3

OA is D
let prob B=x
prob A=2x
Atleast one of the events A and B,
the cases are:
A and not B :2x(prob of A)*(1-x)(prob of not B)
or,
B and not A: x(prob of B)*(1-2x)(prob of not A)
or,
Both A and B: x*2x

Quote:
The probability that at least one of events A and B occurs is 8 times the probability that both events A and B occur.
x(1-2x)+x*2x+2x(1-x)=8*x*2x
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