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PSAT Math Multiple-Choice Practice Question 158

Question: 158

A major hospital conducted a study on a new experimental physical therapy method for some of its patients recovering from knee-replacement surgery. At the beginning of the study, 485 patients who had just had knee-replacement surgery were selected for the study; 194 of the patients were given the experimental physical therapy, and the remaining patients were put into conventional physical therapy. A summary of the recovery times for the patients who were in the study is shown in the table below.
Recovery Time for 485 Patients in the Study
Recovery TimeExperimental TherapyConventional Therapy
6 months or less82151
More than 6 months112140

If a patient in the study is selected at random, which of the following is closest to the probability that the patient will have a recovery time of more than 6 months?

Correct Answer: C

Explanation:

C

The question asks for the probability a patient in the study selected at random will have a recovery time of more than 6 months. Probability is defined as . Read the table carefully to find the right numbers to set up the probability. Because the question states that a patient in the study is selected at random, the total # of possible outcomes is the total number of patients in the study, which is 485. Because the question asks for the probability that the patient will have a recovery time of more than 6 months, the # of outcomes that fit the requirement is the total number of patients with a recovery time of more than 6 months. Make sure to include both those in experimental physical therapy and those in conventional physical therapy to get a total of 112 + 140 = 252. Therefore, the probability is . The question says is closest to, so select the closest choice. The correct answer is (C).

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