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 15% of the small-business owners selected both the economy and finding qualified workers as challenges for growth. A small-business owner is randomly selected. 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 as well?

Question

Laci Hogan

Business

22 April, 23:46

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 15% of the small-business owners selected both the economy and finding qualified workers as challenges for growth. A small-business owner is randomly selected. 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 as well?

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Landyn Landry · Answer 1

0.18

Explanation:

Let P (E) = People who think Economy is a challenge = 0.46

P (W) = People who think finding qualified worker is a challenge = 0.37

P (W and E) = People who think both economy and finding worker is a problem = 0.15

P (E/W) = People who think economy is a problem given that finding worker is a challenge to growth as well = P (W and E) / P (W) + P (E) = 0.15/0.46+0.37 = 0.18