Question

If A and B are two independent events, the probability 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. $\frac{1}{4}$
• D. $\frac{1}{5}$

Answer 1

Answer: (A), (C)

$\frac{1}{2}$
$\frac{1}{4}$

Let probability of occurrence of A = x
Let probability of occurrence of A = y
Probability of occurrence 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 = $\frac{1}{4}$ or $\frac{3}{2}$