Question

A retail store is doing a $50 gift card giveaway by selecting 1 customer from a pool of registered customers. The pool of registered customers has males and females of all ages with 52% of the pool being female and 18% of the pool being over the age of 65. The probability of the winner being female or over age 65 (the union of female and over age 65) is 70%.
a. True
b. False

Answer 1

Answer:

False

Explanation:

Given

$P(Female) = 52\%$

$P(Age>65) = 18\%$

Required

Determine $P(Female\ or\ Age>65)$

The events of being a female and over the age of 65 are non-mutually exclusive events.

We know this because the question says the pool is from all ages.

So, the required probability is calculated using:

$P(A\ or\ B) = P(A) + P(B) - P(A\ and\ B)$

In this case, it is:

$P(Female\ or\ Age>65) = P(Female) + P(Age>65) - P(Female\ and\ Age>65)$

This gives:

$P(Female\ or\ Age>65) = 52\% + 18\% - P(Female\ and\ Age>65)$

$P(Female\ or\ Age>65) = 70\% - P(Female\ and\ Age>65)$

Because the pool is from all ages,

$P(Female\ and\ Age>65) > 0\%$

So:

$P(Female\ and\ Age>65) < 70\%$

The solution to this question is b. False