probability of exactly one banjo in a case of 6 is defective

[palmer69]

If 8% of the banjos that are shipped are defective, and there are 6 banjos per case which is a sampling. What is the probability that exactly one out of a case is defective.

I figured out that 0.48 of the banjos in a case would be defective, and I know that the percentage of exactly one being defective would be less than 8%, but how do I figure out what it would be?

Thank you in advance for any help you can give me.
Lori

 

[tkhunny]

Re: probability of exactly one

You should be able to construct Binomial probabilities.

Pr(Defective) = p = 0.08

Pr(Not Defective) = q = 1-p = 1-0.08 = 0.92

Expand: \(\displaystyle (p+q)^{6}\)

Pr(All Six Defective) = \(\displaystyle p^{6}\)

Pr(Five Defective) = \(\displaystyle 6p^{5}q\)

Pr(Four Defective) = \(\displaystyle 15p^{4}q^{2}\)

Pr(Three Defective) = \(\displaystyle 20p^{3}q^{3}\)

Pr(Two Defective) = \(\displaystyle 15p^{2}q^{4}\)

Pr(One Defective) = \(\displaystyle 6pq^{5}\)

Pr(None Defective) = \(\displaystyle q^{6}\)

Your task is to remember where the coefficients come from. 1 6 15 20 15 6 1 -- This should be very familiar.

Your next task would be to pull one of those terms out of your hat without calculating ALL of them.