Question

Let E and F be two independent events. The probability that exactly one of them occurs is $\frac{11}{25}$ and the probability of none of them occurring is $\frac{2}{25}$. If $P\left(T\right)$ denotes the probability of occurrence of the event T, then

• A. $P\left(E\right)=\frac{3}{5},P\left(F\right)=\frac{4}{5}$
• B. $P\left(E\right)=\frac{1}{5},P\left(F\right)=\frac{2}{5}$
• C. $P\left(E\right)=\frac{4}{5},P\left(F\right)=\frac{3}{5}$
• D. $P\left(E\right)=\frac{2}{5},P\left(F\right)=\frac{1}{5}$

Answer 1

Answer: (A), (C)

$P\left(E\right)=\frac{4}{5},P\left(F\right)=\frac{3}{5}$

We have,
$P\left(E\right)+P\left(E\right)-2P(E\cap F)=\frac{11}{25}$
$P(E^C\cap F^C)=(1-P(E\left)\right)(1-P(F\left)\right)=\frac{2}{25}$
Solving these equations, we shall get
$P\left(E\right)=\frac{4}{5},P\left(F\right)=\frac{3}{5}$
or $P\left(E\right)=\frac{3}{5},P\left(F\right)=\frac{4}{5}$