Answer to Question #180277 in Statistics and Probability for Kenichi

Question

Assume that 5% of Samsung's total smartphone production is defective. What is the probability that at least three of the smartphones are defective if ten items are chosen at random from the production line?

Answer 1

p=0.05,q=1-p=0.95

n=10

Probability at least 3 are defective

$P(x\ge 3)=1-P(x<3)=1-[P(X=0)+P(X=1)+P(X=2)]$

$=1-[^{10}C_0(0.050^0(0.95)^{10}+^{10}C_1(0.050^1(0.95)^{9}+^{10}C_2(0.050^2(0.95)^{8}]$

=1-[0.5987+0.3151+0.0746]

=1-0.98843=0.011565