Question

Probability of solving a particular question by person $A$ is $\frac{1}{3}$ and probability of solving that question by person $B$ is $\frac{2}{5}.$ What is the probability of solving that question by at least one of them ?

• A. $\frac{2}{5}$
• B. $\frac{2}{3}$
• C. $\frac{3}{5}$
• D. $\frac{7}{9}$

Answer 1

The correct option is C $\frac{3}{5}$

Probability of solving a particular question by person $A$,
$P\left(A\right)=\frac{1}{3}$
Probability of solving a particular question by person $B$,
$P\left(B\right)=\frac{2}{5}$
$P\left(A^{\prime }\right),P\left(B^{\prime }\right)$ is the probability that $A,B$ does not solve the problem.

$\therefore$ The probability that at least one of them solves the problem
= Problem is solved by $A$ but not by $B$ +Problem is solved by $B$ but not by $A$+ Problem is solved by both of them
$=P\left(A\right)\times P\left(B^{\prime }\right)+P\left(A^{\prime }\right)\times P\left(B\right)+P\left(A\right)\times P\left(B\right)$
$=\frac{1}{3}\times \frac{3}{5}+\frac{2}{5}\times \frac{2}{3}+\frac{1}{3}\times \frac{2}{5}=\frac{3}{5}$