A grocery bag can be classified as either paper or plastic. 87% of grocery bags

Question

A grocery bag can be classified as either paper or plastic. 87% of grocery bags are classified as plastic. ?

(a) Two grocery bags are chosen at random. What is the probability that both grocery bags are plastic??

?(b) Five grocery bags are chosen at random. What is the probability that all five grocery bags are plastic??

?(c) What is the probability that at least one of five randomly selected grocery bags is paper?? Would it be unusual that at least one of five randomly selected grocery bags is paper??

Explanation / Answer

X ~ Binomial (n,p)

Binomial probability distribution is

P(X) = nCx px ( 1 - p)n-x

a)

For n = 2 , p = 0.87

P( X = 2) = 0.872

= 0.7569

b)

For n = 5 , p = 0.87

P( X = 5) = 0.875

= 0.4984

c)

P(At least one grocery bag is paper) = 1 - P( All grocery bag is plastic)

= 1 - 0.4984

= 0.5016

Since probability is greater than 0.05, it would not be unusual that at least one of five randomly

selected grocery bags is paper.

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