Suppose 2% of cotton fabric rolls and 3% of nylon fabric

Chapter 2, Problem 124E

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QUESTION:

Suppose 2% of cotton fabric rolls and 3% of nylon fabric rolls contain flaws. Of the rolls used by a manufacturer, 70% are cotton and 30% are nylon. What is the probability that a randomly selected roll used by the manufacturer contains flaws?

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QUESTION:

Suppose 2% of cotton fabric rolls and 3% of nylon fabric rolls contain flaws. Of the rolls used by a manufacturer, 70% are cotton and 30% are nylon. What is the probability that a randomly selected roll used by the manufacturer contains flaws?

ANSWER:

Step 1 of 2

We have given  of cotton fabric rolls and  of nylon fabric rolls contain flaws.

Of the rolls,  are cotton and  are nylon.

We are asked to find the probability that a randomly selected roll used by the manufacturer contains flaws.

Let  denote the event that a roll contains a flaw.

Let  denote the event that a roll contains is a cotton.

According to the question, we need to find the probability that the roll contains flaws given that rolls are cotton and nylon.

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