The table given below shows the ages of 75 teachers in a school.

Age (in years) 18−29 30−39 40−49 50−59

No. of teachers 5 25 35 10

Here 18−29 means from 18 to 29, including both.
A teacher from the school is chosen at random. What is the probability that the teacher chosen is
(i) 40 or more than 40 years old?
(ii) 49 or less than 49 years old?
(iii) 60 or more than 60 years old?

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Solution

Total number of teachers = 75
(i) Number of teachers who are 40 or more than 40 years old = 35 + 10 = 45
Let E₁ be the event that the selected teacher's age is 40 years or more.

∴ Required probability = P(E₁) = $\frac{45}{75} = \frac{3}{5}$ 60360 = 16

(ii) Number of teachers who are 49 or less than 49 years old = (35 + 25 + 5) = 65
Let E₂ be the event that the selected teacher's age is 49 years or less.
∴ Required probability = P(E₂) = $\frac{65}{75} = \frac{13}{15}$ 80360 = 29

(iii) Number of teachers who are 60 or more than 60 years old = 0
Let E₃ be the event that the selected teacher's age is more than 60 years.

∴ Required probability = P(E₃) = $\frac{0}{75} = 0$ 0360 =0360360 = 1

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Age (in years)	18−29	30−39	40−49	50−59
No. of teachers	5	25	35	10