Question

If the probability of hitting a target by a shooter, in any shot, is $\frac{1}{3}$, then the minimum number of independent shots at the target required by him so that the probability of hitting the targetat least once is greater than $\frac{5}{6}$, is :

• A. $6$
• B. $5$
• C. $4$
• D. $3$

Answer 1

The correct option is B $5$

$1{-}^n{C}_0{\left(\frac{1}{3}\right)}^0{\left(\frac{2}{3}\right)}^n>\frac{5}{6}$

$\frac{1}{6}>{\left(\frac{2}{3}\right)}^n\Rightarrow 0.1666>{\left(\frac{2}{3}\right)}^n$

$n_{min}=5$