Q. 215.0( 1 Vote )

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?

Answer :

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) =


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