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(From CollegeBoard.com)

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Question

A special lottery is to be held to select the student who will live in the only deluxe room in a dormitory. There are 100 seniors, 150 juniors, and 200 sophomores who applied. Each senior’s name is placed in the lottery 3 times; each junior’s name, 2 times; and each sophomore’s name, 1 time. What is the probability that a senior’s name will be chosen?

Answer Choices

  • (A) 1/8
  • (B) 2/9
  • (C) 2/7
  • (D) 3/8
  • (E) 1/2

Results Summary

In the Selects Univeristy SAT Prep Course, every question type is explained thoroughly first, and then later students are taught how to quickly answer these types of questions, to most efficiently use their time on the SAT Reasoning Test.

For the above question, students will learn the underlying principles of the question types:

When you see the word “probability”, immediately think of either a percentage or a fraction. In this case, all the answers are fractions, meaning we will use fractions to solve this problem.

First, we want to determine how many times a senior’s name will be entered into the draw. If there are 100 students, and each student gets entered 3 TIMES, we know we must multiply (times) these numbers. 3 x 100 seniors = 300 seniors.

The total number of students from which the draw will occur includes the juniors and sophomores as well. Using the same method as above, we determine that there are 2 x 150 juniors, and 1 x 200 sophomores. We want to know the TOTAL number of students, so we will add these values to the seniors. 300 seniors + 300 juniors + 200 sophomores = 800 total students.

Given these values, we see the probability that a senior’s name will be chosen as the number of seniors (300) in the draw over the total number of students (800). 300 seniors / 800 total students.

In its simplest form, 300/800 becomes 3/8. The answer D is correct.

Students will then learn how to streamline the solution process:

100 seniors get 3 entries each…3 x 100 = 300

150 juniors get 2 entries each…2 x 150 = 300

200 sophomores get 1 entry each…1 x 200 = 200

Total = 800

We need the total number of senior entries…300 In simplest form -> 3

And the total number of all entries…800 In simplest form -> 8

Answer

Our answer is D, 3/8.


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