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?

Question

For two events A and B, if \(P(A) = P(A/B) = \frac{1}{4}\) and \(P(B/A) = \frac{1}{2}\), then which of the following is not true?

Answer 1

Alternative Method:

Total number of persons in the group = 5

Step 1: Identify favourable cases directly

We want the probability that the spokesperson is
male OR over 35 years of age.

From the given data:

Number of males = 3
Number of persons over 35 years = 2
Number of males over 35 years = 1

Step 2: Use direct counting (inclusion–exclusion idea)

Number of persons who are either male or over 35 =

(Number of males) + (Number over 35) − (Number of males over 35)

= 3 + 2 − 1

= 4

Step 3: Find probability

Probability =

(Number of favourable persons) / (Total number of persons)

= 4 / 5

Final Answer:

The probability that the spokesperson will be either male or over 35 years of age is
4 / 5

Solution and Explanation