Question

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

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.

Answer 1

a) Choosing a card that is an ace and a four is mutually exclusive. b) Choosing a card that is a diamond and a king is not mutually exclusive. c) Choosing a card that is a king and a heart is not mutually exclusive. d) Choosing a card that is a heart and an odd number is mutually exclusive.

Step-by-step explanation:

Events are mutually exclusive if they cannot occur at the same time. Let's analyze each event:

a) Choosing a card that is an ace and a four: These two events cannot happen simultaneously because a card cannot be both an ace and a four at the same time. Therefore, they are mutually exclusive.

b) Choosing a card that is a diamond and a king: These two events can happen at the same time if the card drawn is the King of Diamonds. Therefore, they are not mutually exclusive.

c) Choosing a card that is a king and a heart: These two events can happen at the same time if the card drawn is the King of Hearts. Therefore, they are not mutually exclusive.

d) Choosing a card that is a heart and an odd number: These two events cannot happen at the same time because a card cannot be both a heart and an odd number. Therefore, they are mutually exclusive.