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Question

From the employees of a company, 5 persons are selected to represents them in the managing committee of the company. Particulars of five persons are as follows:
S. No.NameSexAge in years1HarishM302RohanM333SheetalF464AliceF285SalimM41
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?

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Solution

Here total number of persons = 5
One spokesperson is selected out of 5 person in 5C1=5 ways.
Let A be the event that person is male and B be the event that person is over 35 years.
there are 3 male and one person can be selected in 3C1 ways.
P(A)=3C15C1=35
There are 2 persons who are over 35 years. So one operson can be selected in 2C1 ways.
P(B)=2C15C1=25
There is 1 person who is male and over 35 years.
P(AB)=1C15C1=15
Now P (either male or over 35 years) =P(AB)=P(A)+P(B)P(AB)=35+2515=3+215=45.


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