In a town of 6000 people, 1200 are over 50 years old, and 2000 are females. It is known that 30% of the females are over 50 years. What is the probability that a randomly chosen individual from the town is either female or over 50 years?
let A denote the event that the chosen individual is female and B denote the event that the chosen individual is over 50 years old.
Given : Town consists of 6000 people, 1200 are over 50 years old, and 2000 are females
To find : Probability that a randomly chosen individual from the town is either female or over 50 years = P(A or B)
The formula used : Probability =
P(A or B) = P(A) + P(B) - P(A and B)
For the event A ,
There are 2000 females present in a town of 6000 people
Favourable number of outcomes = 2000
Total number of outcomes = 6000
P(A) = =
For the event B,
There are 1200 are over 50 years of age in a town of 6000 people
Favourable number of outcomes = 1200
Total number of outcomes = 6000
P(A) = =
30% of the females are over 50 years
For the event A and B,
females are over 50 years of age
Favourable number of outcomes = 600
P(A and B) = =
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) =
P(A or B) =
P(A or B) =
The probability that a randomly chosen individual from the town is either female or over 50 years = P(A or B) =