Question

In a shooting competition, the probability that Rahul will hit the target is $\frac{5}{7}$ and the probability that Sheela will hit the target is $\frac{3}{4}$. So what is the probability that both of them will hit the target?

Answer 1

To find the probability both will hit the target.

Let,

$$\begin{gathered} P\left(R\right)=\mathrm{Probability}\mathrm{that}\mathrm{Rahul}\mathrm{hits}\mathrm{the}\mathrm{target}=\frac{5}{7} \\ P\left(S\right)=\mathrm{Probability}\mathrm{that}\mathrm{Sheela}\mathrm{hits}\mathrm{the}\mathrm{target}=\frac{3}{4} \end{gathered}$$

Now,

$\mathrm{Probability}\mathrm{of}\mathrm{both}\mathrm{of}\mathrm{them}\mathrm{hitting}\mathrm{the}\mathrm{target}=P\left(R\right)\times P\left(S\right)=\frac{5}{7}\times \frac{3}{4}=\frac{15}{28}$

Hence, the probability that both will hit the target is $\frac{15}{28}$.