Login/Sign Up
Home » 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?
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?
CBSE | Class 11 | Exercise 31B | Maths | Probability Distribution | RS Aggarwal
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

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) = 1200/6000 =1/5

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) =  600/6000  =1/10

P(A or B) = P(A) + P(B) – P(A and B)

P(A or B) = 13/20

P(A or B) = 13/20

P(A or B) = 13/20

The probability that a randomly chosen individual from the town is either female or over 50 years = P(A or B) = 13/20

i

More Material