An immigration agent sampled cars going from country M to country N. In his report, he indicated that of the 85 cars sampled, 27 cars were driven by women, 53 cars were driven by citizens of country M, 41 cars had two or more passengers, 23 cars were driven by women who are citizens of country M, 22 cars were driven by women and had two or more passengers, 18 cars were driven by citizens of country M and had two or more passengers, and 13 cars were driven by women who are citizens of country M and had two or more passengers. After his supervisor reads the report, she explains to the agent that he made a mistake. Explain how his supervisor knew that the agent's report contained an error.

Question

Mathematics

Maddison Gross

17 July, 15:30

An immigration agent sampled cars going from country M to country N. In his report, he indicated that of the 85 cars sampled, 27 cars were driven by women, 53 cars were driven by citizens of country M, 41 cars had two or more passengers, 23 cars were driven by women who are citizens of country M, 22 cars were driven by women and had two or more passengers, 18 cars were driven by citizens of country M and had two or more passengers, and 13 cars were driven by women who are citizens of country M and had two or more passengers. After his supervisor reads the report, she explains to the agent that he made a mistake. Explain how his supervisor knew that the agent's report contained an error.

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Wood · Answer 1

the numbers of women drivers are inconsistent

Step-by-step explanation:

Let W, C, P stand for the conditions that the drivers were women, the drivers were citizens, and the car had passengers, respectively.

We are told the number of WCP cars is 13, the number of WC cars is 23, and the number of WP cars is 22. The total of WC and WP cars counts WCP cars twice, so the total of cars in these three categories combined is ...

WC + WP - WCP = 23 + 22 - 13 = 32

This number (32) is more than the total number of cars with women driving (27), so there is obviously a mistake.