Question

A candidate is selected for the interview of management trainees for 3 companies. for the first company therefore are 12 candidates for the second there are 15 candidates and fro the third, there are 10 candidates.
find the probability that he is selected in at least one of the companies.

Answer 1

Let $A,B$ and $C$ be the events that the candidate is selected in the 1st , 2nd and 3rd company respectively,

then $P\left(A\right)=\frac{1}{12}$, $P\left(B\right)=\frac{1}{15}$ and $P\left(C\right)=\frac{1}{10}$

$\therefore$ required probability $=1-P\left(\overline{A}n\overline{B}n\overline{C}\right)$

$=1-(1-\frac{1}{12})(1-\frac{1}{15})(1-\frac{1}{10})$

$=1-(\frac{11}{12}\times \frac{14}{15}\times \frac{9}{10})$

$=\frac{23}{100}$