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?
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
A die is thrown. Describe the following events:
(i) \(A: a\) number less than \(7\)
(ii) \(B: a\) number greater than \(7\)
(iii) \(C: a\) multiple of \(3\)
(iv) \(D: a\) number less than \(4\)
(v) \(E: a\) even number greater than \(4\)
(vi) \(F: a\) number not less than \(\)\(3\)
Also, find \(A∪B, A∩B, B∪C, E∩F, D∩E, A-C, D-E, E∩F', F'\)
An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events: \(A:\) the sum is greater than \(8\), \(B:\)\(2\) occurs on either die \(C:\)The sum is at least \(7\), and a multiple of \(3\). Which pairs of these events are mutually exclusive?