SOLUTION: Sweetwater & Associates write weekend trip insurance at a very nominal charge. Records show that the probability that a motorist will have an accident during the weekend and file a

Algebra ->  Probability-and-statistics -> SOLUTION: Sweetwater & Associates write weekend trip insurance at a very nominal charge. Records show that the probability that a motorist will have an accident during the weekend and file a      Log On


   

Question 726752: Sweetwater & Associates write weekend trip insurance at a very nominal charge. Records show that the probability that a motorist will have an accident during the weekend and file a claim is 0.05. Suppose they wrote 15 policies for the coming weekend, what is the probability that exactly two claims will be filed?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
This is a binomial distribution problem.

In this case, n = 15, p = 0.05 and k = 2


So plug all of that into the formula below and evaluate.

P(X = k) = (n C r)*(p)^(k)*(1-p)^(n-k)

P(X = 2) = (15 C 2)*(0.05)^(2)*(0.95)^(15-2)

P(X = 2) = (105)*(0.05)^(2)*(0.95)^13

P(X = 2) = (105)*(0.0025)*(0.5133420832795)

P(X = 2) = 0.13475229686087

P(X = 2) = 0.134752

Final Answer (Rounded to 6 decimal places):

P(X = 2) = 0.134752