Question

A grocery bag can be classified as either paper or plastic. Suppose that 85​% 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) Four grocery bags are chosen at random. What is the probability that all four grocery bags are plastic​? ​(c) What is the probability that at least one of four randomly selected grocery bags is paper​? Would it be unusual that at least one of four randomly selected grocery bags is paper​?

Answer 1

Answer:

a) 0.7225

b) 0.5220

c) 0.478

It is not unusual.

Step-by-step explanation:

Probability grocery bags are plastic = 85% = 0.85

a) If two grocery bags are chosen at random, the probability that both grocery bags are plastic would be:

$^2C_2 (0.85)^2 (1-0.85)^0$

$= (0.85)^2 = 0.7225$

b) If four bags are chosen at random, the probability that all are plastic:

$^4C_4 (0.85)^4 (1-0.85)^0$

$= (0.85)^4 = 0.5220$

Probability all four bags chosen randomly are plastic bags is 0.5220

c) The probability that at least one of four randomly selected grocery bags is paper:

Let's first check for the probability of getting a paper bag.

P(paper bag) = 1 - 0.85 = 0.15

Probability of getting a paper bag is 0.15

Probability that at least one of four randomly selected grocery bags is paper would be:

$1 - ^4C_0(0.15)^0 (0. 85)^4$

$= 1 - (1)(0.85)^4$

$= 1 - 0.5220$

$= 0.478$

Since the probability that at least one bag is paper, 0.478 is greater than 0.05, it is not unusual.