Question

The probabilities of solving a problem by three students $A,B$ and $C$ are $\frac{1}{2},\frac{3}{4}$ and $\frac{1}{4}$ respectively. The probability that the problem will be solved is

• A. $\frac{3}{32}$
• B. $\frac{3}{16}$
• C. $\frac{29}{32}$
• D. None of the above

Answer 1

Answer: (C)

$\frac{29}{32}$

Given, $P\left(A\right)=\frac{1}{2},P\left(B\right)=\frac{3}{4},P\left(C\right)=\frac{1}{4}$
$\Rightarrow P\left(\overline{A}\right)=\frac{1}{2},P\left(\overline{B}\right)=\frac{1}{4},P\left(\overline{C}\right)=\frac{3}{4}$
$\therefore$ Required probability $=1-P(\overline{A}\cap \overline{B}\cap \overline{C})=1-\frac{1}{2}\times \frac{1}{4}\times \frac{3}{4}=\frac{29}{32}$