22
QuizMultiple Choice

Probability in the Business Setting

Question 22 • FowU - Financial Math - B

Perry is considering trying to open a new business within the next few years, and he is doing research to determine what kind of businesses tend to be successful. So far, he has compiled two tables. The first shows the number of businesses of several types started in Perry’s city over the course of two years, and the number of those businesses which did not succeed and were forced to shut down within two years of opening. The second deals with separate records of successful new businesses, showing how much profit those new businesses turned over two years. Businesses on the boundary lines fall in the lower category. Type Food Retail Financial Service Opened 3,193 2,280 1,898 5,045 Closed 1,977 1,626 1,443 3,548 Up to $25k $25-50k $50-75k $75-100k Over $100k Food 945 623 601 258 114 Retail 813 548 347 188 63 Financial 316 244 195 86 51 Service 979 739 432 174 124 Using the tables as experimental data, determine whether it is more likely for a new food establishment to succeed and earn up to $25,000, or whether it is more likely for a new financial establishment to succeed and earn profits in either the $25,000-50,000 range or the $50,000-75,000 range, and how much more likely the one situation is than the other. Express all probabilities as percentages to two decimal places, and express differences by number of percentage points (for example, 23% is 5 percentage points greater than 18%).

Answer
A
The situation involving the food establishment has a probability 11.14 percentage points higher than the situation involving the financial establishment.
B
The situation involving the financial establishment has a probability 12.03 percentage points higher than the situation involving the food establishment.
C
The situation involving the food establishment has a probability 2.08 percentage points higher than the situation involving the financial establishment.
D
The situation involving the financial establishment has a probability 4.99 percentage points higher than the situation involving the food establishment.

Explanation

The profit table lists successful businesses, so compare the requested profit shares among successful businesses. For food, the share earning up to $25,000 is 945 ÷ (945 + 623 + 601 + 258 + 114) = 37.15%. For financial businesses, the share earning $25,000–$75,000 is (244 + 195) ÷ (316 + 244 + 195 + 86 + 51) = 49.22%, about 12.06 percentage points higher. Choice B is the closest match, though its stated difference of 12.03 points is slightly off using the table totals.

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