Question

A classroom contains 10 students. A student committee of 3 (president, vice-president, and treasurer) must be...

A classroom contains 10 students. A student committee of 3 (president, vice-president, and treasurer) must be selected. Harry Potter will serve only as president only if either of his friends Ron Weasley or Hermione Granger serve as vice president; otherwise he leaves the group. The others (including Ron and Hermione) have no such restrictions. What is the probability that Ron or Hermione become the president of this group?

Math   Statistics-And-Probability   
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Answer #1

Probability = Favorable outcomes / Total Outcomes

We break the favorable outcomes into 2 parts

(a) When Harry is the president.

Number of ways of choosing the VP = 2C1 = 2

Number of ways of choosing treasurer = 8C1 = 8

Therefore number of ways = 1 * 2 * 8 = 16

(a) When Harry is not the president.

Then number of ways of choosing president = 9C1 = 9 (excluding harry)

Number of ways of choosing the VP = 9C1 = 9 (including harry as he can be the VP)

Number of ways of choosing treasurer = 8C1 = 8

Therefore number of ways = 9 * 9 * 8 = 648

Therefore total favorable outcomes = 648 + 16 = 664

Total outcomes = 10C1 * 9C1 * 8C1 = 10 * 9 * 8 = 720 (No restrictions)

Therefore the required probability = 664 / 720 = 83 / 90 = 0.922

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