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) =

Rate this question :

If A and B are mutually exclusive events, then

Mathematics - ExemplarState whether the statements are True or False

The probability of an occurrence of event A is .7 and that of the occurrence of event B is .3 and the probability of occurrence of both is .4.

Mathematics - ExemplarIf P (A ∪ B) = P (A ∩ B) for any two events A and B, then

Mathematics - ExemplarState whether the statements are True or False

The probability of intersection of two events A and B is always less than or equal to those favourable to the event A.

Mathematics - Exemplar