A national survey of small-business owners was conducted to determine the challe

Question

A national survey of small-business owners was conducted to determine the challenges for growth for their businesses. The top challenge, selected by 46% of the small-business owners, was the economy. A close second was finding qualified workers (37%). Suppose 12% of the small-business owners selected both the economy and finding qualified workers as challenges for growth. A small-business owner is randomly selected.

a. What is the probability that the owner believes the economy is a challenge for growth if the owner believes that finding qualified workers is a challenge for growth?
b. What is the probability that the owner believes that finding qualified workers is a challenge for growth if the owner believes that the economy is a challenge for growth?
c. Given that the owner does not select the economy as a challenge for growth, what is the probability that the owner believes that finding qualified workers is a challenge for growth?
d. What is the probability that the owner believes neither that the economy is a challenge for growth nor that finding qualified workers is a challenge for growth?

*(Round your answer to 4 decimal places.)
**(Round your answer to 2 decimal places.)

Explanation / Answer

P(Economy) = 0.46

P(Qualified workers) = 0.37

P(economy and qualified workers) = 0.12

A) P(economy| qualified workers) = 0.12/0.37 = 0.3243

B) P(qualified workers | economy) = 0.12/0.46 = 0.2609

C) P( qualified workers | not economy)

= (0.37-0.12)/(1-0.46)

= 0.4630

D) P(neither economy nor qualified workers)

= 1 - (0.46+0.37-0.12)

= 0.71

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