Keiths Florists has 15 delivery trucks used mainly to delive

Keith’s Florists has 15 delivery trucks, used mainly to deliver flowers and flower arrangements in the Greenville, South Carolina, area. Of these 15 trucks, 6 have brake problems. A sample of 5 trucks is randomly selected. What is the probability that 2 of those tested have defective brakes? (Round your answer to 4 decimal places.)

Solution

Probability of an event A = No. of events favorable to that event, i.e. N(A) / No. of total outcomes (N)

Here, the no. of ways a sample of 5 trucks can be selected from a total of 15 trucks, N
     = 15C5 = 15! / (5! * 10!) = 3003

To select 2 defective trucks, we have to select 2 defective trucks out of 6 defective trucks and 3 perfect trucks out of 9 perfect trucks. The no. of ways we can do so, N(A)
     = 6C2 * 9C3 = 6! / (2! * 4!) * 9! / (3! * 6!) = 15 * 84 = 1260

Therefore, the probability that 2 of those tested have defective brakes = N(A) / N = 1260/3003 = 0.4196