Question

A survey of 64 informed voters in Kenya revealed the following information:

45 believe that Voting is a waste of time

49 believe that they have been abducted by space aliens

42 believe both of these things

REQUIRED

i). How many believe neither of these things?

ii). How many believe Voting is a waste of time but don't believe that they have been

abducted by space aliens?​

Answer 1

i) 12 believe neither of these things.

ii) 3 believe voting is a waste of time but don't believe that they have been abducted by space aliens.

Explanation:

I'm going to solve these question treating these events as Venn sets.

I am going to say that:

Event A: Voting is a waste of time.

Event B: They have been abducated by space aliens.

45 believe that Voting is a waste of time

This means that
`A = 45`

49 believe that they have been abducted by space aliens

This means that
`B = 49`

42 believe both of these things

This means that
`A \cap B = 42`

i). How many believe neither of these things?

Total of 64.

At least one is:

`A \cup B = A + B - A \cap B`

With the values we have

`A \cup B = 45 + 49 - 42 = 52`

None:

`64 - 52 = 12`

12 believe neither of these things.

ii). How many believe Voting is a waste of time but don't believe that they have been abducted by space aliens?​

This is:

`A - B = A - (A \cap B) = 45 - 42 = 3`

3 believe voting is a waste of time but don't believe that they have been abducted by space aliens.