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marusya05 [52]
3 years ago
14

A retail store is doing a $50 gift card giveaway by selecting 1 customer from a pool of registered customers. The pool of regist

ered 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
Business
1 answer:
Pani-rosa [81]3 years ago
6 0

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 <em>b. False</em>

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