Question

Eight identical slips of paper, each containing one number from one to eight, inclusive, are mixed up inside a bag. Subset A of the sample space represents the complement of the event in which the number 6 is drawn from the bag.
Which shows subset A?

A = {6}
A = {1, 3, 5, 7}
A = {1, 2, 3, 4, 5, 7, 8}
A = {1, 2, 3, 4, 5, 6, 7, 8}

Answer 1

Answer:  The correct option is (C) A = {1, 2, 3, 4, 5, 7, 8}.

Step-by-step explanation: Given that eight identical slips of paper, each containing one number from one to eight, inclusive, are mixed up inside a bag.

The sample space, S will be

S = {1, 2, 3, 4, 5, 6, 7, 8}.

Subset A of the sample space represents the complement of the event in which the number 6 is drawn from the bag.

Let, 'B' represents the event in which the number 6 is drawn from the bag.

So, B = {6}.

Since 'A' is the complement of 'B', so the set 'A' will contain those element of the sample space 'S' that are not in the set 'B'.

Therefore,

A = B' = {1, 2, 3, 4, 5, 7, 8}

⇒ A = {1, 2, 3, 4, 5, 7, 8}.

Thus, (C) is the correct option.

Answer 2

I will assume that it is a single slip then subset A = {1,2,3,4,5,7,8} (i.e. "1 is drawn", "2 is drawn" etc.)

which is the complement of A^c = {6} ("6 is drawn")

The answer is A = {1,2,3,4,5,7,8}