Question

a) A machine that produces stampings for car engines is not working properly and
producing 15% defectives. The defective and no defective stampings proceed from the
machine on a random manner. If 4 stampings are randomly collected, find the probability
that 2 of them are defective.
b) A person sells 5 cars. The probability that each car will rise in price is 0.6.
What is the probability that three out of the five cars will rise in price?

Answer 1

a)

X ~ binomial (n,p)

Where n = 4 , p = 0.15

P(X) = ⁿC_x p^x (1-p)^n-x

So

P(X = 2) = ⁴C₂ 0.15² 0.85²

= 0.0975

b)

X ~ binomial (n,p)

Where n = 5 , p = 0.60

P(X) = ⁿC_x p^x (1-p)^n-x

So,

P( X = 3) = ⁵C₃ 0.6³ 0.4²

= 0.3456