Question

In a locality, out of 5000 people residing, 1200 are above 30 years of age and 3000 are females. Out of the 1200 who are above 30, two hundred are females. Suppose, after a person is chosen you are told that the person is a female. What is the probability that she is above 30 years of age?
A.$\dfrac{1}{{10}}$
B.$\dfrac{1}{5}$
C.$\dfrac{1}{{15}}$
D.none

Answer 1

Hint: Here we need to find the probability of a female to be above 30 years of age. First we will find the number of people who are under 30 years of age. Then we will find the number of females who are under 30 years of age. Then we will find the probability of a female to be above 30 years of age which is equal to ratio of number of females to the total number of females.

Complete step-by-step answer:
Here we need to find the probability of females to be above 30 years of age.
As it is given that there are a total 3000 females out of 5000.
It is also given that 1200 people are above 30 years of age and out of 1200 people 200 are females.
Number of females who are above 30 years of age $ = 200$
Number of females who are under 30 years of age $ = 3000 - 200 = 2800$
We know that the total number of females $ = 3000$
Therefore the probability of a female to be above 30 years of age will be equal to the ratio of the number of females above 30 years of age to the total number of females.
Required probability $ = \dfrac{{200}}{{3000}}$
On further simplification, we get
$ \Rightarrow $ Required probability $ = \dfrac{1}{{15}}$
Hence, the probability of a female to be above 30 years of age is equal to $\dfrac{1}{{15}}$.
Hence, the correct option is option C.

Note: Here we have obtained the probability of a female to be above 30 years of age, so we need to know about probability and its properties. Probability is defined as the ratio of the required number of outcomes to the total number of outcomes. The value of probability cannot be greater than 1 and the value of probability cannot be negative. Also, we need to remember that the probability of a sure event is always one.