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 $= P \left( A ' BC \right)+ P \left( AB ' C \right)+ P \left( ABC '\right)$
$=1 / 2 \times 1 / 4 \times 1 / 3+1 / 2 \times 3 / 4 \times 1 / 3+1 / 2 \times 1 / 4 \times 2 / 3$
$=1 / 24+1 / 8+1 / 12$
$=(1+3+2) / 24$
$=1 / 4$