Question

A problem is given to three students whose chances of solving it are $\frac{1}{4},\frac{1}{5}$ and $\frac{1}{3}$ respectively. Find the probability that the problem is solved.

Answer 1

Let the 3 student be $A,B,C$ .

Probality that question is solved by $A=P\left(A\right)$

Probality that question is solved by $B=P\left(B\right)$

Probality that question is solved by $C=P\left(C\right)$

Therefore the probability that question is not solved by $A=1-P\left(A\right)$

Therefore the probability that question is not solved by $B=1-P\left(B\right)$

Therefore the probability that question is not solved by $C=1-P\left(C\right)$

Given $P\left(A\right)=\frac{1}{4}$

$P\left(B\right)=\frac{1}{5}$

$P\left(C\right)=\frac{1}{3}$

Hence , the probality that question is not solved $=(1-P\left(A\right))(1-P\left(B\right))(1-P\left(C\right))$

Probability that question is not solved $=(1-\frac{1}{4})(1-\frac{1}{5})(1-\frac{1}{3})$

Thus probability that question is being solved $=1-$ Probality that question is being not solved.

Probality that question is being solved $=1-\frac{2}{5}=\frac{3}{5}$