Question

A man is bowling and the probability of him knocking all the pins is 0.3. If he has 10 shots, what is the probability that hell knock all the pins down less than 3 times?

Answer 1

Let $X=$ the number of times a man knocks all the pins down: $X\sim Bin(n, p).$

Given $n=10, p=0.3, q=1-p=0.7.$

$$P(X<3)=P(X=0)+P(X=1)+P(X=2)$$

$$=\dbinom{10}{0}(0.3)^{0}(0.7)^{10-0}+\dbinom{10}{1}(0.3)^{1}(0.7)^{10-1}$$

$$+\dbinom{10}{2}(0.3)^{2}(0.7)^{10-2}=0.3827827864$$