Question

One hundred sixty people were surveyed and asked if believed in ufos, ghosts, and bigfoot. 42 believed in ufos 45 believed in ghosts 21 believed in bigfoot 11 believed in ufos and ghosts 6 believed in ghosts and bigfoot 4 believed in ufos and bigfoot 2 believed in all three how many people surveyed believed in at least one of these ?

Answer 1

`P(A\cup B \cup C)=89`

Explanation:

From the question we are told that:

Believed in UFO's
`A=42`

Believed in Ghosts
`B=45`

Believed in Bigfoot
`C=21`

Believed in UFO's & Ghosts
`A&B=11`

Believed in Ghosts & Bigfoot
`B&C=6`

Believed in UFO's & Bigfoot
`A&B=4`

Believed in ALL
`A&B&C=2`

Generally with a well detailed Set diagram of the Number of People that that believed in at least one of them is mathematically given by

`P(A\cup B \cup C)=n(A\cap C)-n(B\cap C) +n(A\cap B \cap C)`

`P(A\cup B \cup C)=42+45+21-11-6-4+2`

`P(A\cup B \cup C)=89`