Question

Suppose that 43% of a town's population have blue eyes, 46% have blonde hair, and 24% have both blue eyes and blonde hair. What is the probability that a randomly selected individual in the town will have blue eyes or blonde hair?

Answer 1

We need to find the probability of the event:

having blue eyes or blond hair

This event is the union of the events:

A: having blue eyes.

B: having blond hair.

So, we need to find the probability P(A ∪ B). In order to do so, we can use the following formula:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

We know that the probability of the intersection of A and B (having both) is

P(A ∩ B) = 24%

Also:

P(A) = 43%

P(B) = 46%

Then, using those values into the above formula, we find:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

P(A ∪ B) = 43% + 46% - 24%

P(A ∪ B) = (43 + 46 - 24)%

P(A ∪ B) = 65%