Question

Of 256 consumers polled, some like only thriller movies, some prefer just comedies, and some like both. If 78 people like only thrillers, and 116 like both, how many people prefer only comedies

Answer 1

62.

Explanation:

256-78-116=62

Simple subtraction.

Answer 2

ANSWER

The number of people who like only comedies is


`n(C \cup \: T ' ) = 62`

EXPLANATION

The total number of consumers polled is


`n(C \cup \: T) = 256`

The number of consumers who like both Comedies and Thrillers is


`n(C \cap \: T) = 116`

The number of people who like thrillers is


`n(T) = 116 + 78 = 194`

The number of people who like comedies can be calculated using the formula,


`n(C \cup \: T) = n(C ) + n(T) - n(C \cap \: T)`
We substitute the above values to obtain,


`256= n(C ) +194- 116`


`256= n(C ) +78`


`256 - 78= n(C )`


`n(C ) = 178`

The number of people who like only comedies


`n(C \cup \: T ' ) = 178 - 116`


`n(C \cup \: T ' ) = 62`