SAT Math Multiple Choice Question 446: Answer and Explanation

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Test Information

Question: 446

Registered to Vote? 1 2 3 4 5 Total
Yes 112 104 228 487 163 1,094
No 28 76 48 158 54 364
Total 140 180 276 645 217 1,458

11. An incumbent state senator (currently in office and running for an additional term) conducts a survey to see how favorably the people in her district view her. In the survey, responses of 1 or 2 represent an unfavorable view, a response of 3 is a neutral view, and responses of 4 or 5 are favorable. The results of the survey are recorded in the table. If one registered voter is chosen at random to attend a town hall meeting, what is the probability that the voter does not view the senator unfavorably?

  • A. 40.6%
  • B. 59.4%
  • C. 78.1%
  • D. 80.3%

Correct Answer: D

Explanation:

D

Difficulty: Hard

Category: Problem Solving and Data Analysis / Statistics and Probability

Strategic Advice: Whenever a question involves a two-way table, read carefully to see which rows and/or columns you need to focus on. Here, the politician is only targeting registered voters for the town hall meeting, so focus on the "Yes" row in the table.

Getting to the Answer: The question asks for the probability that the registered voter chosen will not view the senator unfavorably. This means the voter's view is either neutral or favorable, so look at columns 3, 4, and 5. Add the numbers together to get 228 + 487 + 163 = 878. The probability that you're looking for is the quotient of this number divided by the total number of registered voters: 878 รท 1,094 = 0.8025, or approximately 80.3%.

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