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Let E and F be two independent events. T...

Let `E and F` be two independent events. The probability that exactly one of them occurs is `11/25` and the probability if none of them occurring is `2/25`. If `P(T)` denotes the probability of occurrence of the event `T ,` then (a) `P(E)=4/5,P(F)=3/5` (b) `P(E)=1/5,P(F)=2/5` (c) `P(E)=2/5,P(F)=1/5` (d) `P(E)=3/5,P(F)=4/5`

A

`P(E)=4/5,P(F)=3/5`

B

`P(E)=1/5,P(F)=2/5`

C

`P(E)=2/5,P(F)=1/5`

D

`P(E)=3/5,P(F)=4/5`

Text Solution

Verified by Experts

The correct Answer is:
A, D
Let `P(E)=eand P(F)=f`
`P(EuuF)-P(EnnF)=11/25`
`impliese+f-2ef=11/25" "(1)`
`P(barEnnbarF)=2/25`
`implies(1-e)(1-f)=2/25" "(2)`
From (1) and (2),
`ef=12/25and e+f=7/5`
Solving, we get
`e=4/5,f=3/5or e=3/5,f=4/5`
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