Video: Deciding If Events Are Mutually Exclusive

Amelia has a deck of 52 cards. She randomly selects one card and considers the following events: Event A: picking a card that is a heart. Event B: picking a card that is black. Event C: picking a card that is not a spade. Are events A and B mutually exclusive? Are events A and C mutually exclusive? Are events B and C mutually exclusive?

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Video Transcript

Amelia has a deck of 52 cards. She randomly selects one card and considers the following events. Event A, picking a card that is a heart. Event B, picking a card that is black. Event C, picking a card that is not a spade. Are events A and B mutually exclusive? Are events A and C mutually exclusive? Are events B and C mutually exclusive?

Let’s take each one of these questions in turn, starting with the first one. Are events A and B mutually exclusive? Event A is picking a card that is a heart, and event B is picking a card that is black. If we consider a standard deck of 52 cards, event A would be selecting any one of the cards that is hearts. And this is event B, picking a card that is black.

In mutually exclusive events, the probability of A and B is zero. It’s not possible for both events to happen at the same time. When we’re asking, “Are A and B mutually exclusive?,” we should ask, can A and B happen at the same time? Can Amelia choose a card that is a heart and black? No, that is not possible. Since it’s not possible for A and B to be true at the same time, these events are mutually exclusive.

What about events A and C? Event A is the same. Because event C involves picking a card that is not a spade, it could be clubs, hearts, or diamonds. We ask the same question. Can event A and event C happen at the same time? That is possible. Since they can both be true at the same time, these events are not mutually exclusive.

What about B and C? With the same question, can B and C happen at the same time? It is possible to choose a card that is black and is not a spade. Those would be any cards that are clubs. Because event B and C can happen at the same time, they’re not mutually exclusive.

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