Question

Following are the ages (in years) of 360 patients, getting medical treatment in a hospital:

Age (in years)	10−20	20−30	30−40	40−50	50−60	60−70
Number of patients	90	50	60	80	50	30

One of the patients is selected at random.
Find the probability that his age is
(i) 30 years or more but less than 40 years
(ii) 50 years or more but less than 70 years
(iii) less than 10 years
(iv) 10 years or more

Answer 1

Total number of patients = 360
(i) Number of patients whose age is 30 years or more but less than 40 years = 60

Let E₁ be the event that the selected patient's age is in between 30 - 40.

∴ P(patient's age 30 is years or more but less than 40 years) = P(E₁) = $\frac{60}{360}=\frac{1}{6}$

(ii) Number of patients whose age is 50 years or more but less than 70 years = (50 +30) = 80

Let E₂ be the event that the selected patient's age is in between 50 - 70.
∴ P(patient's age is 50 years or more but less than 70 years) = P(E₂) = $\frac{80}{360}=\frac{2}{9}$

(iii) Number of patients whose age is less than 10 years = 0

Let E₃ be the event that the selected patient's age is less than 0.

∴ P(patient's age is less than 10 years)= P(E₃) = $\frac{0}{360}=0$

(iv) Number of patients whose age is 10 years or more = 90 + 50 + 60 + 80 + 50 + 30 = 360

Let E₄ be the event that the selected patient's age is 10 years or more. Then
∴ P(patient's age is 10 years or more) = P(E₄) = $\frac{360}{360}=1$