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The probability of simultaneous occurren...

The probability of simultaneous occurrence of at least one of two events A and B is p. If the probability that exactly one of A, B occurs is q then prove that `P( A )+P( B )=2-2p+qdot`

A

`2-2p+q`

B

`2+2p-q`

C

`3-3p+q`

D

`2-4p+q`

Text Solution

Verified by Experts

The correct Answer is:
A
Since, P(exactly one of A, B occurs) = q (given), we get
`P(A uu B) - P (A nn B) = q`
`rArr " " p-P(A nn B)=q`
`rArr " " P(A nn B) = p -q`
`rArr " " 1-P(A' uu B') = p-q`
`rArr " " P(A' uu B') = 1-p+q`
`rArr P(A')+P(B')-P(A' nn B')=1+q-p`
`rArr " " P(A')+P(B')=(1-p+q)+[1-P (A uu B)]`
`" " (1-p+q)+(1-p)`
`" " 2-2p+q`
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