Question

The probability of the occurrence of two independent events ($A$ and $B$) is known to be each greater than $\frac{1}{2}$. Its given that probability of the occurrence of the second event is $\frac{3}{25}$. Also the probability of the occurrence of second simultaneously with the first not occurring is $\frac{8}{25}$. Find the probability of the events.

• A. $P\left(A\right)=\frac{4}{5}$, $P\left(B\right)=\frac{3}{5}$
• B. $P\left(A\right)=\frac{4}{25}$, $P\left(B\right)=\frac{4}{25}$
• C. $P\left(A\right)=\frac{3}{5}$, $P\left(B\right)=\frac{4}{5}$
• D. $P\left(A\right)=\frac{3}{25}$, $P\left(B\right)=\frac{4}{25}$

Answer 1

The correct option is C $P\left(A\right)=\frac{3}{5}$, $P\left(B\right)=\frac{4}{5}$

$P(A\cap \overline{B})=\frac{3}{25}=P\left(A\right)-P\left(A\right)P\left(B\right)$ ...(1)

$P(\overline{A}\cap B)=\frac{8}{25}=P\left(B\right)-P\left(A\right)P\left(B\right)$ ...(2)
From (1) and (2)
$P\left(A\right)=\frac{3}{5},P\left(B\right)=\frac{4}{5}$