Answer to Question #191070 in Civil and Environmental Engineering for Joshua

Question

The probability that a certain product is defective is 0.35. Find the probability that exactly 3 of the next 5 products taken is non-defective.

Answer 1

Binomial distribution is used

Probability of r defective from n products

p(r)=nCr(p)^(r)q^(n-r)

Probability of exactly 3 defective from 5 products

p(3)=5C3(0.35)^(3)q^(5-3)

p(3)=10(0.35)^(3)(1-0.35)^(5-3)

p(3)=10(0.35)^(3)(0.65)^(2)

p(3)=10(0.35)^(3)(0.65)^(2)

p(3)=0.1811

Thus probability of exactly 3 not defective is 1-0.1811=0.81