Question

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 A. `P(E )=1//3,P(F)=1//4` B. `P(E )=1//2,P(E )=1//6` C. `P(E )=1//6,P(F )=1//2` D. `P(E )=1//4,P(F)=1//3` Select the correct answer from above options

Answer 1

Correct Answer - A::B Both E and F happen `rArr P(E nn F) = (1)/(12)` and neither E nor F happens `rArr P(bar(E) nn bar(F)) = (1)/(2)` But for independent events, we have `P(E nn F) = P(E) P(F) = (1)/(12) " ….(i)` and `P(bar(E) nn bar(F)) = P(bar(E)) P(bar(F))` `= {1-P(E)} {1-P(F)}` ` = 1-P(E) -P(F) + P(E) P(F)` `rArr (1)/(2) = 1-{P(E) + P(F)}+ (1)/(12)` `rArr P(E) + P(F) = 1-(1)/(2) + (1)/(12) = (7)/(12) " "... (ii)` On solving Eqs. (i) and (ii), we get either `P(E) = (1)/(3) "and " P(F) = (1)/(4)` `"or " P(E) = (1)/(4) "and" P(F) = (1)/(3)`