Question

You work for a company that makes umbrellas. After being produced, the umbrellas are randomly packaged in units of 12 and shipped to retailers. Your employer is interested to know about the probability with which a customer will receive a package with any number of faulty umbrellas. You know that the probability that any given umbrella is faulty is 0.37, use this information to answer the following questions. 6. A) What is the probability that none of the umbrellas are faulty? B) What is the probability that half of the umbrellas are faulty? C) What is the probability that all of the umbrellas are faulty?

Answer 1

6: Let X is a random variable shows the number of defective umbrellas. Here X has binomial distribution with parameters n=12 and p=0.37.

(a)

The probability that none of the umbrella is faulty is

$P(X=0)=\binom{12}{0}(0.37)^{0}(1-0.37)^{12-0}=0.0039$

(b)

The probability that half of the umbrellas is faulty is

$P(X=6)=\binom{12}{6}(0.37)^{6}(1-0.37)^{12-6}=0.1482$

(c)

The probability that all of the umbrellas is faulty is

$P(X=12)=\binom{12}{12}(0.37)^{12}(1-0.37)^{12-12}=0.0000066$