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Problem-Solving and Data Analysis Difficulty: Medium

At a movie theater, there are a total of $350$ customers. Each customer is located in either theater A, theater B, or theater C. If one of these customers is selected at random, the probability of selecting a customer who is located in theater A is $0.48$ , and the probability of selecting a customer who is located in theater B is $0.24$ . How many customers are located in theater C?

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Explanation

Choice D is correct. It’s given that at a movie theater, there are a total of $350$ customers and that each customer is located in either theater A, theater B, or theater C. If the probability of selecting a customer in theater A is $0.48$ , then $left parenthesis 0.48 right parenthesis left parenthesis 350 right parenthesis$ , or $168$ , customers are located in theater A. If the probability of selecting a customer in theater B is $0.24$ , then $left parenthesis 0.24 right parenthesis left parenthesis 350 right parenthesis$ , or $84$ , customers are located in theater B. It follows that there are $168 plus 84$ , or $252$ , customers in theater A and theater B. Therefore, there are $350 minus 252$ , or $98$ , customers in theater C.

Choice A is incorrect. This is the percent, not the number, of the customers that are located in theater C.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect. This is the number of customers that are located in theater B, not theater C.