Question

1. Two percent of the picture puzzles made by the Shoddy Toy Company (STC) are missing some pieces. A picture puzzle addict buys five STC puzzles. Explain why it is reasonable to use a binomial probability mass function for the number of defective puzzles among the five that were purchased and find the parameters n and p. Then find the probability that at least 2 are defective.

Answer 1

There is a fixed number of trials, i,e, n = 5

probability of success(defective) = 2% = 2/100 = 0.02

number of outcomes is only two, either success(defective) or failure(non defective)

each trail is independent

So, Binomial probability mass function is appropriate for use

we have n = 5, p = 0.02 and r = 2(defective)

Using binomial formula  

P(at least 2) = 1- P(x=0)-P(x=1)

And

This implies

P(at least 2) = 1- 0.9039 - 0.0922

= 1 - 0.9961

= 0.0039