PSAT Math Multiple-Choice Question 405: Answer and Explanation

Question: 405

Based on the table, if a single applicant is selected at random from all the applicants, what is the probability that he or she will have a 2-year degree and be at least 26 years old?

• A.
• B.
• C.
• D.

Correct Answer: B

Explanation:

B

Difficulty: Hard

Category: Probability

Getting to the Answer: The first criterion is fairly straightforward—the applicant must have a 2-year degree, so focus on that column in the table. The second criterion is a bit trickier—at least 26 years old means 26 years old or older, so you'll need to use the values in the rows for 26–35, 36–45, and Older than 45. There were 19 in the 26–35 age group who had a 2-year degree, 13 in the 36–45 age group, and 2 in the Older than 45 age group, resulting in a total of 19 + 13 + 2 = 34 out of 112 applicants. The probability of randomly selecting one applicant from any of these three groups is , which reduces to , so (B) is correct.