Dev can hit a target 3 times in 6 shots pawan can hit the target 2 times in 6 shots and Lakhan can hit the target 4 times in 4 shots. What is the probability that at least 2 shots hit the target -
Correct Answer: $$\frac{{2}}{{3}}$$
Probability of hitting the target:
Dev can hit target ⇒ $$\frac{{3}}{{6}}$$ =$$\frac{{1}}{{2}}$$
Lakhan can hit target =$$\frac{{4}}{{4}}$$ = 1
Pawan can hit target = $$\frac{{2}}{{6}}$$ = $$\frac{{1}}{{3}}$$
Required probability that at least 2 shorts hit target
$$\eqalign{ & = \frac{1}{2} \times \frac{2}{3} + \frac{1}{2} \times \frac{1}{3} + \frac{1}{2} \times \frac{1}{3} \cr & = \frac{1}{3} + \frac{1}{6} + \frac{1}{6} \cr & = \frac{4}{6} \cr & = \frac{2}{3} \cr} $$
Dev can hit target ⇒ $$\frac{{3}}{{6}}$$ =$$\frac{{1}}{{2}}$$
Lakhan can hit target =$$\frac{{4}}{{4}}$$ = 1
Pawan can hit target = $$\frac{{2}}{{6}}$$ = $$\frac{{1}}{{3}}$$
Required probability that at least 2 shorts hit target
$$\eqalign{ & = \frac{1}{2} \times \frac{2}{3} + \frac{1}{2} \times \frac{1}{3} + \frac{1}{2} \times \frac{1}{3} \cr & = \frac{1}{3} + \frac{1}{6} + \frac{1}{6} \cr & = \frac{4}{6} \cr & = \frac{2}{3} \cr} $$
