Question

The probability of solving a problem by three persons $A,B$ and $C$ independently is $\frac{1}{2}$, $\frac{1}{4}$ and $\frac{1}{3}$ respectively. Then the probability of the problem is solved by any two of them is

• A. $\frac{1}{12}$
• B. $\frac{1}{4}$
• C. $\frac{1}{24}$
• D. $\frac{1}{8}$

Answer 1

Answer: (B)

Required probability $=P\left(A^{\prime }BC\right)+P\left(A{B}^{\prime }C\right)+P\left(AB{C}^{\prime }\right)$
$=1/2\times 1/4\times 1/3+1/2\times 3/4\times 1/3+1/2\times 1/4\times 2/3$
$=1/24+1/8+1/12$
$=(1+3+2)/24$
$=1/4$