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Probability and conditional probability SAT question
Math · Problem-Solving and Data Analysis · Medium · Answer it here, explanation included.
For a science project, Anka recorded whether it rained each weekday and weekend day for 12 weeks. Her results are summarized in the table below.
| Rain | No rain | Total | |
| Number of weekdays | 12 | 48 | 60 |
| Number of weekend days | 8 | 16 | 24 |
| Total | 20 | 64 | 84 |
If one of the days on which there was no rain is selected at random, what is the probability the day was a weekend day?
ExplanationShow
Choice B is correct. There were 64 days with no rain. It was a weekend day for 16 of those 64 days. So 16 out of 64 of the days with no rain were weekend days. Because the day is selected at random, each day has an equal chance of being selected, so the probability is 
.
Choice A is incorrect. It is the probability that a day selected at random from any one of the days during the 12 weeks is a weekend day with no rain. Choice C is incorrect. It is the probability that a day selected at random from the weekend days has no rain. Choice D is incorrect. It is the probability that a day selected at random from the days with no rain is a weekday.
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