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Question
In a town of 8000 people, 1300 are over 50 years and 3000 are females. It is known that 30% of the females are over 50 years. What is the probability that a chosen individual from the town is either a female or over 50 years?
Solution
Total number of people in a town is 8000.
n(S) = 8000
Total number of females = 3000
Let A be the event of getting number of females
n(A) = 3000
P(A) = `("n"("A"))/("n"("S")) = 3000/8000`
Number of people over 50 years = 1300
Let B be the event of getting number of people over 50 years.
n(B) = 1300
P(B) = `("n"("B"))/("n"("S")) = 1300/8000`
Given 30% of the females are over 50 years.
30% of 3000 = `30/100 xx 3000` = 900
n(A ∩ B) = 900
P(A ∩ B) = `("n"("A" ∩ "B"))/("n"("S"))`
= `900/8000`
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
= `3000/8000 + 1300/8000 - 900/8000`
= `(3000 + 1300 - 900)/8000`
= `3400/8000`
= `34/80`
= `17/40`
Proability of getting either a female or over 50 years = `17/40`
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