Management Aptitude Test Feb 2012 Paper

(3) P(A) = Probability that A hits the target = $\frac{4}{5}$
P(R) = Probability that R hits the target = $\frac{3}{4}$
P(C) = Probability that C hits the target = $\frac{2}{3}$
Required probability
= P $\stackrel{-}{\left(\mathit{A}\right)}$ (P(B) P(C) + P(A)P $\stackrel{-}{\left(\mathit{B}\right)}$ P(C) + P(A)P(B)P $\stackrel{-}{\left(\mathit{C}\right)}$ + P(A)P(B)P(C)
= $\frac{1}{5}\cdot \frac{3}{4}\cdot \frac{2}{3}$ + $\frac{4}{5}\cdot \frac{1}{4}\cdot \frac{2}{3}$ + $\frac{4}{5}\cdot \frac{3}{4}\cdot \frac{1}{3}$ + $\frac{4}{5}\cdot \frac{3}{4}\cdot \frac{2}{3}$
= $\frac{6+8+12+24}{60}$ = $\frac{50}{60}=\frac{5}{6}$