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The probability of event A is 3//4. The ...

The probability of event `A` is `3//4`. The probability of event `B`, given that event `A` occurs is `1//4`. The probability of event `A`, given that event `B` occurs is `2//3`. The probability that neither event occurs is

A

`(1)/(6)`

B

`(27)/(112)`

C

`(5)/(32)`

D

`(1)/(8)`

Text Solution

Verified by Experts

The correct Answer is:
C
`P(A) = (3)/(4) , P(B//A) = (1)/(4), P(A//B) = (2)/(3) , P (A^(c)nn B^(c))`= ?
`therefore P(B//A) = = (p(BnnA))/(P(A)) = (1)/(4)` (given)
`P(B nn A) = (3)/(4) (1)/(4) = (3)/(16)`
Now , `P(A//B) = (P (AnnB))/(P(B)) = (2)/(3)` (given)
`therefore P(B) = (3)/(2) .(3)/(16) = (9)/(32)`
`therefore P(A or B) = (3)/(4) + (9)/(32) - (3)/(16) = (24 + 9 - 6)/(32) = (27)/(32)`
`therefore P(A^(c) nn B^(c) ) = 1 - P(A or B) = 1 - (27)/(32) = (5)/(32)`
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