Question

A grocery bag can be classified as either paper or plastic. 84​% 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 eight randomly selected grocery bags is paper​?

Answer 1

Given that, A grocery bag can be classified as paper or plastic 84% of grocery bags are classified as plastic So, Plgrocery bag is plastic) = 0.84 Pl grocery bag is papers = 1-0.84 = 0.16 Let y be random variable denotes the number of bags. That are plastic Here, n=2 þ= 0.84 XN Binomial (n=2, p=0.84) The probability man function of xis, P(x= x) = 12) (0.84" (1-0.845 ; 2=0,112 x 2-1 P (both grocery bags are plastic) = P(x=2) - (²) 10.845 (0.163 = (0 (0.845 (01) - o. Post

S-X b) Here, nas p=0.84 - *~ Binomial (n=S, P=0.84) The probability mam function of xis, P(X=x) = (5) (0.84* (1-0.845 : x=0,1,2-05 Plall five grocery bags are plastic) = P(x=5) = (5) 10.843 (1-0.84) = (1) co.org co o. 4182119424 ł 0..4182 Nond -) Rete dodagi cepend Plat least one of tive randomly) of bag is grocery bag is paper = 1- P(All five bags are plastic) = 1-0.4182 [from part 0] = 0.50818 :, Plat least one of five rondomly selected bags is paper) = 0.5818 No It would not be unusual that at at least one of rondomly selected five the grocery bags is paper because probability is greater than 0.05