A high school class consists of 6 seniors, 10 juniors, 11 sophomores, and 5 freshmen. Exactly 2 of the juniors are male, and exactly 5 of the sophomores are female.  If two students are randomly selected from this class, what is the probability that the pair consists of a female junior and a male sophomore?

Question
Asked Feb 25, 2019

A high school class consists of 6 seniors, 10 juniors, 11 sophomores, and 5 freshmen. Exactly 2 of the juniors are male, and exactly 5 of the sophomores are femaleIf two students are randomly selected from this class, what is the probability that the pair consists of a female junior and a male sophomore?

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Expert Answer

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Step 1

From the given problem, we have:

6 seniors, 10 juniors, 11 sophomores, and 5 freshmen

Total number of students = 6 + 10 + 11 + 5 = 32

There are exactly 2 of the juniors are male and exactly 5 of the sophomores are females.

Female juniors = 10 – 2 = 8

Male sophomore = 11 – 5 = 6

Step 2

We need to find the probability that the pair consists of a female junior and a male sophomore.

Probability of choosing female junior first then a male sophomore

P(female junior chosen, then a male sophomore) = 8/32 x 6/31 = 3/62 

Probability of choosing male sophomore first then female junior

P(male sophomore first then female junior) = 6/32 x 8/31 = 3/62 

Step 3

So,

The probability that the pair consists of a female junior and a male sophomore = P(female junior chosen, then a male sophomore) + P(male sophomore fi...

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Math

Probability

Basic Probability

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