Question

A company manufactures washers, about 5% of which are defective. If a random sample
of 100 washers are inspected, what is the probability that fewer than 4 are defective?

Answer 1

fewer than 4 defective ---> 0 ,1,2, or 3 are defective
prob(defective) = 5/100 = 1/20
prob(not defective) = 19/20

prob
= C(100,0) (1/20)^0 (19/20)^100 + C(100,1)(1/20)(19/20^99 + C(100,2)(1/20)^2 (19/20)^98 + C(100,3)(1/20)^3 (19/20)^97
= .00592.. + .03116.. + .08118...+ .13957..
= .2578...

check my arithmetic