Answer to Question #116165 in Statistics and Probability for Samuel

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 tue probability at least one fuse will be defective ? (b) . What is tue probability that more than one fuse will be defective given that at level one is defective ?

Answer 1

Binomial distribution problem with $P=0.05$ and $n=6$

(a). $P(1\le)$

$P(1\le)=1-P(=0)$

$P(=0) = (1-0.05)^6=0.735092$

$P(1\le)=1-0.735092=0.264908$

(b). $P(1<|1\le)$

$P(>1|≥1)=P(>1)/P(≥1)$

$P(>1)=1-P(=0)-P(=1)=1-0.735-0.232=0.033$

$P(>1|≥1)=0.033/0.265=0.124$