sat suite question viewer

Problem-Solving and Data Analysis / Probability and conditional probability Difficulty: Medium

Weekday and Weekend Day Rain for 12 Weeks
	Rain	No rain	Total
Number of weekdays	12	48	60
Number of weekend days	8	16	24
Total	20	64	84

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.

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?

A. $the fraction 4 over 21$

B. $the fraction 1 over 4$

C. $the fraction 2 over 3$

D. $the fraction 3 over 4$

Back question 22 of 46 Next

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

Explanation

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 $the fraction 16 over 64, equals the fraction 1 over 4$ .

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.