Question

Arun and Tarun appeared for an interview for two vacancies. The probability of Arun's selection is $\frac{1}{4}$ and that of Tarun's rejection is $\frac{2}{3}$. Find the probability that at least one of them will be selected.

Answer 1

Let $A$ be event of Arun Selection.

$T$ be event of Tarun`s Selection.

$P\left(A\right)=\frac{1}{4}$ ; $P\left(T\right)=\frac{1}{3}$

Required probability $=1-P\left(\overline{A}\right)P\left(\overline{T}\right)=1-(1-\frac{1}{4})\left(\frac{2}{3}\right)=\frac{1}{2}$