Question

If $A$ and $B$ are two independent events, the probabilty that both $A$ and $B$ occur is $\frac{1}{8}$ and the probability that neither of them occurs is $\frac{3}{8}$. The probability of the occurrence of $A$ is:

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{6}$
• D. $\frac{1}{5}$

Answer 1

The correct option is A $\frac{1}{2}$

Let probability of occurence of $A=x$
Let probability of occurence of $B=y$
Probability of occurence of both $=xy=\frac{1}{8}$
Probability that both will not occur $=(1-x)(1-y)=\frac{3}{8}$
Therefore,
$x+y=\frac{3}{4}$
$y=\frac{3}{4}-x$
Substituting in the above equation,
$(\frac{3}{4}-x)x=\frac{1}{8}$
$8x^2-6x+1=0$
$x=\frac{1}{4}\text{or}\frac{1}{2}$