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

1 answer
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

Answers

Answer:FalseExplanation:Given[tex]P(Female) = 52\%[/tex][tex]P(Age>65) = 18\%[/tex]RequiredDetermine [tex]P(Female\ or\ Age>65)[/tex]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:[tex]P(A\ or\ B) = P(A) + P(B) - P(A\ and\ B)[/tex]In this case, it is:[tex]P(Female\ or\ Age>65) = P(Female) + P(Age>65) - P(Female\ and\ Age>65)[/tex]This gives:[tex]P(Female\ or\ Age>65) = 52\% + 18\% - P(Female\ and\ Age>65)[/tex][tex]P(Female\ or\ Age>65) = 70\% - P(Female\ and\ Age>65)[/tex]Because the pool is from all ages,[tex]P(Female\ and\ Age>65) > 0\%[/tex]So:[tex]P(Female\ and\ Age>65) < 70\%[/tex]The solution to this question is b. False

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