Home
Class 12
MATHS
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`
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY II

    CENGAGE ENGLISH|Exercise SINGLE CORRECT ANSWER TYPE|28 Videos

  • PROBABILITY I

    CENGAGE ENGLISH|Exercise JEE Advanced|7 Videos

  • PROGRESSION AND SERIES

    CENGAGE ENGLISH|Exercise ARCHIVES (MATRIX MATCH TYPE )|1 Videos

Similar Questions

Explore conceptually related problems

E and F are two independent events. The probability that both e and F happen is 1/12 and the probability that neither E nor F happens is 1/2. Then

If E and F are independent events, then write P (E uu F)

If P(E) = 0.25 , What is the probability of not E .

If E and F are independent events such that 0 lt P(E) lt 1 and 0 lt P(F) lt 1 , then

The Probability that at least one of the events E_(1) and E_(2) will occur is 0.6. If the probability of their occurrence simultaneously is 0.2, then find P(barE_(1))+P(barE_(2))

If A and B are independent events such that P(A)=p ,\ P(B)=2p\ a n d\ P (Exactly one of A and B occurs ) =5/9 , find the value of pdot

If E and F are two independent events and P(E)=1/3,P(F)=1/4, then find P(EuuF) .

Ea n dF are two independent events. The probability that both Ea n dF happen is 1/12 and the probability that neither Ea n dF happens is 1/2. Then, A) P(E)=1//3, P(F)=1//4 B) P(E)=1//4, P(F)=1//3 C) P(E)=1//6, P(F)=1//2 D) P(E)=1//2, P(F)=1//6

If A and B are independent events such that P(A)=p, P(B)=2p and P(Exactly one of A,B) =5/9 , then find p.

Let A and B be two independent events with P(A) = p and P(B) = q. If p and q are the roots of the equation ax^(2) + bx + c = 0 , then the probability of the occurrence of at least one of the two events is