Question

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

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

Answer 1

The correct option is C $\frac{3}{4}$

Let $A,B,C$ respectively denote the events that the problem is solved by $A,B,C$ respectively.

$P\left(A\right)=\frac{1}{2},P=\overline{\left(A\right)}=\frac{1}{2},P\left(B\right)=\frac{1}{3},P\overline{\left(B\right)}=\frac{2}{3}$
$P\left(C\right)=\frac{1}{4},P\overline{\left(C\right)}=\frac{3}{4}$
Problem will be solved if even one of them solve it So, the first we calculate probability that is not solved $P\overline{\left(A\right)}P\overline{\left(B\right)}P\overline{\left(C\right)}=\frac{1}{2}\times \frac{2}{3}\times \frac{3}{4}=\frac{1}{4},$
The required probability $=1-\frac{1}{4}=\frac{3}{4}.$