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`