ProbabilityHard
Question
Let E and F be two independent events. The probability that both E and F happen is 1/ 12 and the probability that neither E. nor F happen is 1 /2. Then,
Options
A.P(E) = 1/ 3, P(F) = 1/ 4
B.P(E) = 1/ 2, P(F) = 1/ 6
C.P(E) = 1/ 6, P(F) = 1/ 2
D.P(E) = 1/ 4, P(F) = 1/ 3
Solution
Both E and F happen ⇒ P(E ∩ F) = 
and neither E nor F happens ⇒ P(
∩ 
) = 
But for independent events, we have
P(E ∩ F) = P(E) P(F) = ......(i)
and P(
∩ 
) = P() P()
= {1- P(E)} {1- P(F)}
= 1- P(E) - P(F) + P(E)P(F)
⇒
= 1 - {P(E) + P(F)} + 
⇒ P(E) + P(F) = 1 -
......(ii)
On solving Eqs. (i) and (ii) , we get
either P(E)=
and P(F) =
or P(E) = and P(F) =
and neither E nor F happens ⇒ P(
∩ ) = But for independent events, we have
P(E ∩ F) = P(E) P(F) =
......(i) and P(
∩ ) = P() P()= {1- P(E)} {1- P(F)}
= 1- P(E) - P(F) + P(E)P(F)
⇒
= 1 - {P(E) + P(F)} + ⇒ P(E) + P(F) = 1 -
......(ii) On solving Eqs. (i) and (ii) , we get
either P(E)=
and P(F) =or P(E) =
and P(F) =Create a free account to view solution
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