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Question
From the employees of a company, 5 persons are selected to represent them in the managing committee of the company. Particulars of five persons are as follows:
| S. No. | Name | Sex | Age in years |
| 1. | Harish | M | 30 |
| 2. | Rohan | M | 33 |
| 3. | Sheetal | F | 46 |
| 4. | Alis | F | 28 |
| 5. | Salim | M | 41 |
A person is selected at random from this group to act as a spokesperson. What is the probability that the spokesperson will be either male or over 35 years?
Solution
Let A represent selection of male and B represent person's age above 35 years.
Total number of males = 3
Total person above 35 years of age = 2
There is 1 male above 35 years of age.
Total persons are 5. Ways to select one of them = `""^5C_1 = 5`
Ways to select 1 man from 3 men = `""^3C_1 = 3`
∴ P(A) = `(""^3C_1)/(""^5C_1) = 3/5`
Ways to select one person above 35 years = `""^2C_1 = 2`
P(B) = `(""^2C_1)/(""^5C_1) = 2/5`
P(A ∩ B) = `(""^2C_1)/(""^5C_1) = 1/5`
P(A ∪ B) = P(male or person above 35 years)
= P(A) + P(B) − P(A ∩ B)
= `3/5 + 2/5 - 1/5`
= `4/5`
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