Question

You are playing a game with your friend where you flip a coin and roll a number cube.

Let Event A=(coln lands heads up, rolling an even number)
Let Event B = (coin lands heads up, rolling an odd number)
List all elements of the sample space and both subsets.
Elements of the sample space: { (H, 1), (H, 2), (H, 3), (H, 4), (T, 1), (T, 2), (T, 3), (T, 4) }
Elements of Event A: { (H, 2), (H, 4) }
Elements of Event B: { (H, 1), (H, 3) }
What are the elements of AUB?
What are the elements of A∩B?

Answer 1

The sample space is { (H, 1), (H, 2), (H, 3), (H, 4), (T, 1), (T, 2), (T, 3), (T, 4) }. Event A has elements {(H, 2), (H, 4)}. Event B has elements {(H, 1), (H, 3)}. The elements of AUB are {(H, 1), (H, 2), (H, 3), (H, 4)}. The elements of A∩B are {(H, 2)}.

Step-by-step explanation:

The sample space for the experiment of flipping a coin and rolling a number cube is { (H, 1), (H, 2), (H, 3), (H, 4), (T, 1), (T, 2), (T, 3), (T, 4) }.

The elements of Event A, which represents the coin landing heads up and rolling an even number, are {(H, 2), (H, 4)}.

The elements of Event B, which represents the coin landing heads up and rolling an odd number, are {(H, 1), (H, 3)}.

The elements of the union of Event A and Event B (AUB) are {(H, 1), (H, 2), (H, 3), (H, 4)}.

The elements of the intersection of Event A and Event B (A∩B) are {(H, 2)}.