Question

A problem in statistics is given to three students A, B and C whose chances of solving it independently are $\frac{1}{2},\frac{1}{3}$ and $\frac{1}{4}$ respectively. The probability that the problem will be solved is

• A. $\frac{1}{12}$
• B. $\frac{11}{12}$
• C. $\frac{1}{2}$
• D. $\frac{3}{4}$

Answer 1

Answer: (D)

$\frac{3}{4}$

$P$(Problem will be solved)

$=1-P$(Problem will not be solved by $A,B$ and $C$)

$=1-\left[(1-\frac{1}{2})(1-\frac{1}{3})(1-\frac{1}{4})\right]$

$=1-\frac{1}{2}\times \frac{2}{3}\times \frac{3}{4}=1-\frac{1}{4}=\frac{3}{4}$

Hence, D is the correct option.