The probability that A hits a target is 1/3 and the probability that B hits it is 2/5 . What is the probability that the target will be , if each one of A and B shoots at the target?

Explanation

Required probability `=\{P}(\{A} \cup \{B})`


so,


`1-\{P}(\overline{\{A}}) \{P}(\overline{\{B}})`


`\{P}(\overline{\{A}})=1-\frac{2}{3}=\frac{1}{3}`.......(1)


`\{P}(\overline{\{B}})=1-\frac{3}{5}=\frac{2}{5}`


put value in equation (1)


`\Rightarrow 1-P(\bar{A}) P(\bar{B})`


`=1-(\frac{1}{3} \times \frac{2}{5})=\frac{13}{15}`