A survey of 100 TV viewers revealed that over the last year:

1. 34 watched CBS.
2. 15 watched NBC.
3. 10 watched ABC.
4. 7 watched CBS and NBC.
5. 6 watched CBS and ABC.
6. 5 watched NBC and ABC.
7. 4 watched CBS, NBC, and ABC.
8. 18 watched HGTV, and of these, none watched CBS, NBC, or ABC.

Calculate how many of the 100 TV viewers did not watch any of the four channels (CBS, NBC, ABC or HGTV).

• 1
• 37
• 45
• 55
• 82

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: B

C = the set of TV watchers who watched CBS over the last year

N = the set of TV watchers who watched NBC over the last year

A = the set of TV watchers who watched ABC over the last year

H = the set of TV watchers who watched HGTV over the last year

The number of TV watchers in the set [math] C ∪ N ∪ A [/math] is

34 + 15 + 10 – 7 – 6 – 5 + 4 = 45.

Because [math]C ∪ N ∪ A[/math] and [math]H[/math] are mutually exclusive, the number of TV watchers in the set [math]C ∪ N ∪ A ∪ H[/math] is

45 + 18 = 63.

The number of TV watchers in the complement of [math]C ∪ N ∪ A ∪ H[/math] is thus

100 – 63 = 37.

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.