Question

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?

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