Question

bag contains 15 marbles numbered from 1 to 15. Two marbles are selected from the bag at the same time. Let event E = the two numbers do NOT differ by 10 How many outcomes are in the complement of E? A) 5 B) 10 C) 25 D) 200

Answer 1

5!

Explanation:

The complement of E is when the numbers differ by 10,

(1, 11), (2, 12), (3, 13), (4, 14), (5, 15)

Thus, there are 5 outcomes where the numbers differ by 10.

Answer 2

The numbers DO differ by 10 if they are

- 1 and 11
- 2 and 12
- 3 and 13
- 4 and 14
- 5 and 15

Each outcome technically has two ways of occurring, but since we're taking two marbles at a time, that would be the same as saying, for instance, that drawing 1 and 11 is the same as drawing 11 and 1. We only count such an event once.

So the answer is (a) 5.