Problem Solving

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

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

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...

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

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