Find the probability

Question

A package of 6 fuses are tested where the probability an individual fuse is defective is 0.05. (That is, 5% of all fuses manufactured are defective).

(a) What is the probability one fuse will be defective?

(b) What is the probability at least one fuse will be defective?

(c) What is the probability that more than one fuse will be defective, given that at least one is defective?

Answer 1

let p be probability of defective p=0.05

probability not defective is p=1-0.05=.95

a) we use binomial probability n=6, k=1 (6 1)*(0.05)¹*(.95)^(6-1) = 6!/(1!*5!) * 0.05* (.95)⁵ = 6*(0.05)*(.7737)

b) we determine 1- probability of zero fuses defective

for 0 fuses defective, n=6, k=0 (6 0)*(0.05)⁰*(.95)⁶ = (.95)⁶= .735

So probability of at least one defective fuse is 1-.735 = .2649