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PSAT Math Multiple-Choice Practice Question 788

Question: 788

A coffee shop recorded data on the types of beverages ordered by its patrons in a given month. Each patron visited only once during the month and purchased only one beverage. The four listed beverages are the only ones sold at this coffee shop. 
Cappuccino
Espresso
Latte
Americano
Total
Females under 18
230
125
325
170
850
Males under 18
170
185
240
220
815
Females age 18 and older
425
328
530
290
1,573
Males age 18 and older
350
429
477
313
1,569
Total
1,175
1,067
1,572
993
4,807

Assume that the sample in the month portrayed in the table is representative of the coffee shop's sales for an entire year. Based on these assumptions, if a female customer is selected at random, what is the approximate probability that she will purchase a latte?

Correct Answer: A

Explanation:

(A) If the sample is representative of the sales for a year, then we would expect the proportion of females who purchased a latte during the year to be the same as the proportion of females who purchased a latte in the sample. In the sample, there were 850 females under 18 and 1,573 females 18 and over for a total of 2,423 females. Also, 325 females under 18 and 530 females 18 and over purchased lattes, for a total of 855 lattes purchased by females in the sample. Therefore, the probability that a randomly selected female would purchase a latte is given by the following fraction:

Choice (A) is the answer.

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