Question

Paul will roll two standard dice simultaneously. If Event A = both dice are odd and Event B = at least one die is even, which ofthe following best describes events A and B?Select two answers.

Answer 1

The best descriptions for events A and B are:

• Not Mutually Exclusive
• Dependent

Event A: Both dice are odd.

Event B: At least one die is even.

To determine whether events A and B are mutually exclusive, we need to check if they can both occur at the same time (i.e., if there is an outcome where both events A and B are true).

Let's analyze the possibilities:

• For event A to occur, both dice must be odd (e.g., 1 and 3).
• For event B to occur, at least one die must be even (e.g., 2 and 5, or 4 and 3).

Based on the above possibilities, it's clear that there are scenarios where both events A and B can be true simultaneously.

For example, if both dice show the values 1 and 3, both events A and B are satisfied. Therefore, events A and B are not mutually exclusive.

Regarding the independence of events A and B, independence means that the occurrence of one event does not affect the probability of the other event occurring.

In this case, the events are not independent because if event A occurs (both dice are odd), it means that event B cannot occur (neither die is even). Therefore, events A and B are dependent.

Answer 2

For this case the sample space is given by:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,1) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

The events for A are:

(1,1) (3,3) (5,5)

And the events for B are:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,3) (2,5) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,3) (4,5) (5,1) (5.2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,3) (6,5)

Then we can conclude that the answer is:

Not Mutually exclusive