Mathematics, 19.07.2019 20:30 lllamasarebae3076

Agrocery 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?

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Answer from: isudgyia

Probability is used to determine the chances of an event

The probability that both grocery bags are plastic is 0.9409The probability that all five grocery bags are plastic is 0.8587The probability that at least one grocery bags is paper is 0.1413It would not be unusual that at least one of five randomly selected grocery bags is paper.

$p = 97\%$ -- chances that a bag is plastic

(a) Both plastics selected are plastic

This is calculated as:

P(2) = p^2

So, we have:

$P(2) = (97\%)^2$

P(2) = 0.9409

Hence, the probability that both grocery bags are plastic is 0.9409

(b) All five are plastic

This is calculated as:

P(5) = p^5

So, we have:

$P(5) = (97\%)^5$

P(5) = 0.8587

Hence, the probability that all five grocery bags are plastic is 0.8587

The probability that none of the five is paper is the same as the probability that all five is plastic.

So:

P(None) = 0.8587

Using complement rule,

$P(At\ least\ 1) = 1 - P(None)$

So, we have

$P(At\ least\ 1) = 1 - 0.8587$

$P(At\ least\ 1) = 0.1413$

Hence, the probability that at least one grocery bags is paper is 0.1413

The above probability is greater than 0.05

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

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