Sweetwater Associates write weekend trip insurance at a ver

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 0.0006. Suppose they wrote 518 policies for the coming weekend, what is the probability that exactly two claims will be filed?

0.0354

0.0545

0.0441

0.0254

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

P( X = 2 ) = ( 518 2 ) * ( 0.0006^2) * ( 1 - 0.0006 )^516
= 0.0354