Victor owner of Laszlos Mens Haberdashery purchases mens sui

Victor, owner of Laszlo’s Men’s Haberdashery, purchases men’s suits and ties from 15 independent manufacturers, 12 of which have a record of late deliveries. Victor intends to order from eight of those 15 manufacturers to stock his initial inventory. He is concerned that the grand opening may be delayed if his orders include more than six chronically delinquent suppliers. How likely are his fears to be realized? This is a probability based question. I am looking to find out how likely it is for six chronically delinquent suppliers to occur. Please explain all formulas. Thank you.

Solution

How likely are his fears to be realized?

the probability of delayed is 12 / 15 = 0.8

and we will order ( Victor)  eight of those 15 manufacturers to stock his initial inventory n=8

so if we need the probability his orders include more than six chronically delinquent suppliers

is

P( x > 6) = P(x=7) + P(X=8)

P(x=7) = 8C7 * 0.80^7 * 0.20^8-7 =0.3355

P(x=8) = 8C8 * 0.80^8 * 0.20^8-8 =0.1678

P(x>6) = 0.5033