Step-by-step explanation:
To determine the probabilities, we need to calculate the total number of possible committees and the number of committees that satisfy each condition. Let's calculate the probabilities step by step:
(i) Probability of no man:
To form a committee with no man, we need to choose 2 women from the available 2 women. This can be calculated as follows:
Total number of possible committees = C(4, 2) = 6
Number of committees with no man = C(2, 2) = 1
Therefore, the probability of having no man on the committee is 1 out of 6, which can be expressed as 1/6.
(ii) Probability of one man:
To form a committee with one man, we can choose 1 man from the available 2 men and 1 woman from the available 2 women. The calculation is as follows:
Total number of possible committees = C(4, 2) = 6
Number of committees with one man = C(2, 1) * C(2, 1) = 4
Therefore, the probability of having one man on the committee is 4 out of 6, which simplifies to 2/3.
(iii) Probability of two men:
To form a committee with two men, we need to choose 2 men from the available 2 men and no women. The calculation is as follows:
Total number of possible committees = C(4, 2) = 6
Number of committees with two men = C(2, 2) = 1
Therefore, the probability of having two men on the committee is 1 out of 6, which can be expressed as 1/6.
In summary:
(i) Probability of no man = 1/6
(ii) Probability of one man = 2/3
(iii) Probability of two men = 1/6