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Let Ea n dF be tow independent events. T...

Let `Ea n dF` be tow 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)` deontes 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)`

Text Solution

Verified by Experts

The correct Answer is:
A, B

`P(E uu F) - P( E nn F) = (11)/(25) " "…. (i) ["i.e. only E or only F"]`

Neither of them occurs ` = (2)/(25)`
`rArr P(bar(E) nn bar (F)) = (2)/(25) " "...(ii)`
From Eq. (i), `P(E) + P(F) - 2P (E nn F) = (11)/(25) " " .....(iii)`
From Eq. (ii), `(1-P(E))(1-P(F)) = (2)/(25)`
`rArr 1-P(E) - P(F) + P(E) * P(F) = (2)/(25) " "..(iv)`
From Eqs. (iii) and (iv),
`P(E) + P(F) = (7)/(5) "and " P(E) * P(F) = (12)/(25)`
`therefore P(E) * [(7)/(5) - P(E)] = (12)/(25)`
`rArr (P(E))^(2) - (7)/(5) P(E) + (12)/(25) = 0`
`rArr [P(E) - (3)/(5)] [P(E) - (4)/(5)] = 0`
`therefore P(E) = (3)/(5) "or" (4)/(5) rArr P(F) = (4)/(5) " or" (3)/(5)`
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