Misc 8
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:
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?
Total number of persons = 5
So, n(S) = 5
Probability spokesperson is male
Let A be the event that person selected is male
There are 3 males
So, n(A) = 3
Probability spokesperson is male = P(A)
= (𝑛(𝐴))/(𝑛(𝑆))
= 3/5
Probability spokesperson is over 35 years old
Let B be the event that person selected is over 35
There are 2 person over 35 years old
So, n(B) = 2
Probability spokesperson is over 35 years old = P(B)
= (n(B))/(n(S))
= 2/5
We need to find
probability that the spokesperson will be either male or over 35 year
i.e. P(A ∪ B)
We know that
P(A ∪ B) = P(A) +P(B) – P(A ∩ B)
To find P(A ∪ B),
we must find P(A ∩ B) first
P(A ∩ B)
Probability that spokesperson is male & over 35 years old
Here, 1 person is both male & over 35 years old
So, n(A ∩ B) = 1
P(A ∩ B) = (𝑛(𝐴 ∩ 𝐵))/(𝑛(𝑆))
= 1/5
Now,
P(A ∪ B) = P(A) +P(B) – P(A ∩ B)
= 3/5 + 2/5 – 1/5
= (3 + 2 − 1)/5
= 4/5
Hence
Probability that the spokesperson will be either male or over 35 year
= P(A ∪ B)
= 𝟒/𝟓

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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