Question

Find the sample space for a committee of two chosen from Alice (A), Bill (B), Carol (C), and David (D).

A. {(A, B), (C, D)}
B. {A, B, C, D}
C. {(A, B), (A, C), (A, D), (B, C), (B, D), (C, D)}
D. {(A, B), (A, D), (B, C), (C, D)}
Find the sample space if both sexes must be represented.
A. {(A, B), (A, C), (A, D), (B, C), (B, D), (C, D)}
B. {(A, B), (C, D)}
C. {(A, B), (A, D), (B, C), (C, D)}
D. {A, B, C, D}

Answer 1

1. A

2. C

Not 100% sure but its my best guess

Answer 2

(a) C. {(A, B), (A, C), (A, D), (B, C), (B, D), (C, D)}

(b) C. {(A,B),(A,D),(B,C),(C,D)}

Explanation:

Given four members eligible for selection:

Alice (A), Bill (B), Carol (C), and David (D).

The possible combinations are:

(A,B),(A,C),(A,D),(B,A),(B,C),(B,D),(C,A),(C,B),(C,D), (D,A),(D,B), (D,C)

Part A

Since the same pairs are equal i.e. (A, B)=(B , A),

The Sample space for a committee of two is:

{(A,B),(A,C),(A,D),(B,C),(B,D),(C,D)}

This is Option C.

Part B

If both genders must be represented, we remove the entries that contain the same gender from the sample space above.

A and C -Female

B and D - Male

{(A,B),(A,C),(A,D),(B,C),(B,D),(C,D)}

Therefore, the sample space if both genders are to be represented is:

{(A,B),(A,D),(B,C),(C,D)}

This is Option C.