Question

Let $E$ and $F$ be two independent events such that $P\left(E\right)>P\left(F\right)$ . The probability that both $E$ and $F$ happened is $\frac{1}{12}$ and the probability that neither $E$ nor $F$ happens is $\frac{1}{2},$ then

• A. $P\left(E\right)=\frac{1}{3},P\left(F\right)=\frac{1}{4}$
• B. $P\left(E\right)=\frac{1}{2},P\left(F\right)=\frac{1}{6}$
• C. $P\left(E\right)=\frac{1}{2},P\left(F\right)=\frac{1}{8}$
• D. none of these

Answer 1

Answer: (A)

$P E \cap F=P E \cdot P F=\frac{1}{12}, P E^{\prime} \cap F^{\prime}=\frac{1}{2}$
$1-P E 1-P F=\frac{1}{2}$