Question

The table given below shows the age of 80 teachers in a school.

Age in years	18-29	30-39	40-49	50-59
Number of teachers	11	32	30	7

A teacher is chosen at random. What is the probability that the age of the selected teacher is:
A. 18 years or more?
B. Between 30-39 years (including both)?
C. Above 60 years?
D. 40 or more than 40 years?

Answer 1

In this question, we are given ages of teachers and we have to find probability when one of them is chosen. As we know, probability of an event is given as:
$\text{Probability}=\dfrac{\text{Number of favorable outcomes}}{\text{Number of total outcomes}}$
So, for every part, we will find the number of teachers who satisfy a given condition which will become our number of favorable outcomes and the number of total outcomes will be the total number of teachers in the school, so using these we will find probability.

Complete step-by-step answer:
We are given table as:

Age in years	18-29	30-39	40-49	50-59
Number of teachers	11	32	30	7

One of the teachers is chosen at random. So, let us find the probability of age of the total teacher according to given parts.
A. Here we have to find the probability that, age of the teacher is equal to or more than 18 years. From the table, we can see that every teacher's age is 18 years or more. Hence, the number of favourable outcomes will equal the total number of teachers. Since, total number of teachers are 80, so our probability becomes, $\text{Probability}=\dfrac{\text{80}}{\text{80}}=1$
Hence, the probability that the age of the teacher will be 18 years or more is 1.
B. Here we need to find a number of teachers whose age is between 30-39 years to calculate our favorable outcomes. As we can see from the table, 32 teachers lie in the age group 30-39 years. Hence, the number of favorable outcomes becomes 32 and the total outcome is the total number of teachers which is 80. So our probability becomes, $\text{Probability}=\dfrac{\text{32}}{\text{80}}=0.4$
Hence, the probability that the age of the teacher will lie between 30-39 years is 0.4.
C. Here we need to find a number of teachers with age above 60 years, so that this becomes our number of favorable outcomes. As we can see from the table, no teacher's age is more than 60 years. Hence, the number of favorable outcomes is zero and the total number of outcomes are 80. So our probability becomes, $\text{Probability}=\dfrac{0}{80}=0$
Hence, there is 0 probability that the selected teacher's age is more than 60 years.
D. Now, we have to find a number of teachers with age 40 years or more so that it becomes our number of favorable outcomes. As we can see from the table, 40-49 and 50-59 are classes with age more than or equal to 40 years. So, a favorable outcome becomes equal to 30+7 = 37. Also, total outcomes are the total number of teachers that is 80. So probability becomes, $\text{Probability}=\dfrac{37}{80}=0.4625$
Hence, the probability that the selected teacher's age is more than or equal to 40 years is 0.4625.

Note: Students should be careful while calculating favorable outcomes. They should note that for every class both numbers are included in the age. When the probability of any event is zero then it means that there is no chance that event will occur and if probability is 1, this means that event will occur for the same.