Question

A grocery bag can be classified as either paper or plastic. Suppose that 97​% 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​?

Answer 1

Answer with explanation:

Given : The probability of grocery bags are classified as plastic = 0.97

(a) f two bags are chosen at random.

Then , the probability that both grocery bags are plastic​ is given by :-

$^2C_2(0.97)^2(1-0.97)^0=0.9409$

(b) If five grocery bags are chosen at random.

Then , the probability that all five grocery bags are plastic​ is given by :-

$^5C_5(0.97)^5(1-0.97)^0\approx0.8587$

(c) The probability of getting paper = 1-0.97=0.03

The probability that at least one of five randomly selected grocery bags is paper :-

$P(x\geq1)=1-P(0)\\\\1-^5C_0(0.03)^0(0.97)^5\\\\=1-(0.03)^0(0.97)^5=0.1412659\approx0.14>0.05$

Thus , it would not be unusual that at least one of five randomly selected grocery bags is paper.