Question

An arcade game is such that the probability of any person winning is always $\mathrm{0.3.}$ Then the least number of people play the game to ensure that the probability that atleast one person wins is greater than or equal to $0.96$ is

Answer 1

Probability of at least one person wins $\ge 0.96$
$1-P\left(\text{none wins}\right)\ge 0.96$
$P\left(\text{none wins}\right)\le 0.04$
${0.7}^n\le 0.04\Rightarrow n\ge 9$
Hence, least number of people is $9.$