Question

Let E and F be two independent events. The probability that exactly one of them occurs is $\frac{11}{25}$ and the probability that none of them occurs is $\frac{2}{25}$ . Then

• A. P(E) = , P(F) =
• B. P(E) = , P(F) =
• C. P(E) = , P(F) =
• D. P(E) = , P(F) =

Answer 1

Answer: (A), (D)

The correct options are
A

P(E) = , P(F) =

D

P(E) = , P(F) =

Let P(E) = x, p(F) = y

x + y – 2xy = $\frac{11}{25}$, (1 – x)(1 – y) = $\frac{2}{25}$ $\Rightarrow$ xy = $\frac{12}{25}$, x + y = $\frac{7}{5}$

$\Rightarrow$ x = $\frac{4}{5}$, y = $\frac{3}{5}$(or) x = $\frac{3}{5}$, y = $\frac{4}{5}$