Probability - Mutually Exclusive Events

A card is chosen at random from a standard deck of 52 playing cards.

Let:

• Event \(A\): “The card is a heart”
• Event \(B\): “The card is a king”
• Event \(C\): “The card is black”

1. State whether events \(A\) and \(B\) are mutually exclusive.
2. State whether events \(A\) and \(C\) are mutually exclusive.
3. Find \(P(A∪B)\).
4. Determine whether events \(A\) and “not \(A\)” are exhaustive. Explain your answer.
5. Are events \(B\) and \(C\) exhaustive?