Question

The probability of a man hitting a target is 1/2. How many times must he fire so that the probability of hitting the target at least once is more than 90%.

Answer 1

Probability of man hitting a target $=\frac{1}{2}$

Here,

$p=\frac{1}{2}$

The probability of bot hitting the target in n trails is $q^{\ast }$

Therefore to find the smallest n of which the probability of hitting at once in more than 90 %

$1-q^{\ast }>0.9$

$1-{\left(\frac{1}{2}\right)}^{\ast }>0.9$

${\left(\frac{1}{2}\right)}^{\ast }>0.9$

$2^{\ast }>10$

$n>2$

$n=4,5,\mathrm{6.....}$

$Thereforethesmallestn=4$