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Probability and conditional probability SAT question
Math · Problem-Solving and Data Analysis · Hard · Answer it here, explanation included.
Employees working for a customer service line at an electric company recorded all the calls last Monday and noted whether the caller asked for repairs and whether the caller asked about a bill. The results are summarized in the table below.
| Asked for repairs |
Did not ask for repairs |
Total | |
| Asked about a bill |
48 | 623 | 671 |
| Did not ask about a bill |
130 | 90 | 220 |
| Total | 178 | 713 | 891 |
If a caller last Monday who asked about his or her bill is selected at random, which of the following is closest to the probability that the customer also asked for repairs?
ExplanationShow
Choice B is correct. According to the table, a total of 671 customers asked about a bill. Of these, 48 also asked for repairs. Therefore, if a customer who asked about a bill is selected at random, the probability that the customer also asked for repairs is 
.
Choice A is incorrect. This is the probability that a customer selected at random from all customers who called on Monday both asked for repairs and asked about a bill. Choice C is incorrect. This is the probability that a customer selected at random from all customers who called on Monday asked for repairs, regardless of whether or not the customer asked about a bill. Choice D is incorrect. This is the probability that a customer selected at random from those who asked for repairs also asked about a bill.
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