In recent years, business failures in the United States numbered 63509. The chemical industry accounted for 9499 of these business failures.

Question

In recent years, business failures in the United States numbered 63509. The chemical industry accounted for 9499 of these business failures. The Mid-West states accounted for 7900 of the business failures. Suppose that 1270 of all business failures were chemical businesses located in the Mid-West. A failed business is randomly selected from this list of business failures. What is the probability that the business is in the chemical industry if it is known that the business is located in the Mid-West

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1 year 2021-09-03T17:56:20+00:00 1 Answers 2 views 0

0.1608 = 16.08% probability that the business is in the chemical industry if it is known that the business is located in the Mid-West.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$$P(B|A) = \frac{P(A \cap B)}{P(A)}$$

In which

P(B|A) is the probability of event B happening, given that A happened.

$$P(A \cap B)$$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Failed business in the Midwest.

Event B: Chemical industry.

Probability of failed business being in the Mid-West:

7900 out of 63509. So

$$P(A) = \frac{7900}{63509}$$

Probability of a failed business being a chemical industry in the Mid-West.

1270 out of 63509. So

$$P(A \cap B) = \frac{1270}{63509}$$

What is the probability that the business is in the chemical industry if it is known that the business is located in the Mid-West?

$$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{1270}{63509}}{\frac{7900}{63509}} = \frac{1270}{7900} = 0.1608$$

0.1608 = 16.08% probability that the business is in the chemical industry if it is known that the business is located in the Mid-West.