Question

Among a department store’s 15 delivery trucks, five emit excessive amounts of pollutants. If eight of the trucks are randomly picked for inspection, what is the probability that this sample will include at least three of the trucks which emit excessive amounts of pollutants?

Answer 1

Total number of trucks = 15

Number of trucks that emit excessive amounts of pollutants = 5

Number of trucks that does not emit excessive amounts of pollutants = 15 - 5 = 10

Number of ways to select r items from n, nCr = n!/(r! x (n-r)!)

P(at least three of the trucks emit excessive amounts of pollutants) = P(3 trucks emit excessive amounts of pollutants and 5 trucks don't) + P(4 trucks emit excessive amounts of pollutants and 4 trucks don't) + P(5 trucks emit excessive amounts of pollutants and 3 trucks don't)

= (5C3 x 10C5 / 15C8) + (5C4 x 10C4 / 15C8) + (5C5 x 10C3 /15C8)

= (10x252 + 5x210 + 1x120)/6,435

= 0.5734