An insurance company found that 9% of drivers were involved in a car accident last year. If seven drivers are randomly selected, find the probability that exactly two of them were involved in a car accident last year.
Accepted Solution
A:
Answer: 0.1061Step-by-step explanation:Given : An insurance company found that 9% of drivers were involved in a car accident last year.Thus, the probability of drivers involved in car accident last year = 0.09The formula of binomial distribution :-[tex]P(X=x)^nC_xp^x(1-p)^{n-x}[/tex] If seven (n=7) drivers are randomly selected then , the probability that exactly two (x=2) of them were involved in a car accident last year is given by :-[tex]P(X=2)=^7C_2(0.09)^2(1-0.09)^{7-2}\\\\=\dfrac{7!}{2!5!}(0.09)^2(0.91)^{5}=0.106147867882\approx0.1061[/tex]Hence, the required probability :-0.1061