Question

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 `P(E)=4/5,P(F)=3/5` `P(E)=1/5,P(F)=2/5` `P(E)=2/5,P(F)=1/5` `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)` Select the correct answer from above options

Answer 1

Correct Answer - 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)`