Question

A fair, six-sided die is rolled. Describe the sample space S, identify each of the following events with a subset of S, and compute its probability (an outcome is the number of dots that show up).

Event A = the outcome is an even number.
Event B = the outcome is less than four.
The complement of A.
A GIVEN B
B GIVEN A

Answer 1

The sample space S for rolling a fair, six-sided die is {1, 2, 3, 4, 5, 6}. Event A is the outcome is an even number, and Event B is the outcome is less than four. The complement of A is {1, 3, 5}. For A given B, the outcomes in both A and B are {2}.

Step-by-step explanation:

The sample space, S, for rolling a fair, six-sided die is {1, 2, 3, 4, 5, 6}.

Event A = the outcome is an even number, so A = {2, 4, 6}. The probability of event A, P(A), is 3/6 or 1/2.

Event B = the outcome is less than four, so B = {1, 2, 3}. The probability of event B, P(B), is 3/6 or 1/2.

The complement of A is the set of outcomes that are not in A. In this case, the complement of A is {1, 3, 5}. The probability of the complement of A, P(A'), is 3/6 or 1/2.

For A given B, we consider the outcomes that are in both A and B. In this case, A given B is {2}. The probability of A given B, P(A|B), is 1/3.