My wife bought a box of 20 gladiola bulbs from the Greenhous

My wife bought a box of 20 gladiola bulbs from the Greenhouse Nursery. The box states that if fewer than 90 percent of the bulbs germinate, the manufacturer will refund the price of the entire box. Suppose the probability of germination is only 0.8. What is tire probability that my wife will not get a refund on her purchase?

Solution

p = 0.8
q = 1-p = 1-0.8 = 0.2
n = 20
90% of 20 = 18
According to Binomial distribution
P(x) = nCx*p^x*q^(n-x)
Required probability = P(X >/= 18)
= P(x=18)+P(x=19)+P(x=20)
= 20C18*0.8^18*0.2^2 + 20C19*0.8^19*0.2^1 + 20C20*0.8^20*0.2^0
= 0.13691 + 0.05765 + 0.01153
= 0.20609
Therefore, it can be said that the probability of NOT getting a refund = 0.20609