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Suppose you conduct an experiment in which you draw a single card from a standard deck of 52 cards. Which events are mutually exclusive? Select all that apply.

A. Choosing a card that is an ace and a four
B. Choosing a card that is a diamond and a king
C. Choosing a card that is a king and a heart
D. Choosing a card that is a heart and an odd number

1 Answer

4 votes

Final answer:

In a card experiment, mutually exclusive events cannot occur at the same time. The only mutually exclusive event in the options provided is choosing a card that is both an ace and a four, since a single card cannot hold two different ranks.

Step-by-step explanation:

When you conduct an experiment by drawing a single card from a standard deck of 52 cards, certain events are mutually exclusive. Mutually exclusive events cannot happen at the same time. For example, selecting a card that is both a heart and a spade is impossible, as a single card cannot belong to two different suits simultaneously.

Given the options you've provided:

  • A. Choosing a card that is an ace and a four - These are mutually exclusive because a single card cannot be both an ace and a four.
  • B. Choosing a card that is a diamond and a king - Not mutually exclusive since a card can be both a diamond and a king if it is the king of diamonds.
  • C. Choosing a card that is a king and a heart - Not mutually exclusive, as there is a card that is the king of hearts.
  • D. Choosing a card that is a heart and an odd number - Not mutually exclusive because there are odd-numbered heart cards (3, 5, 7, 9).

Therefore, the only mutually exclusive option here is A.

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