Question

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

Answer 1

Answer:

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.

Step-by-step 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.