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.

choosing a card that is an ace and a four
choosing a card that is a diamond and a king
choosing a card that is a king and a heart
choosing a card that is a king and a queen
choosing a card that is a heart and an odd number

choosing a card that is an ace and a four

choosing a card that is a king and a queen

Ah, the wonderful world of cards! Now, let's see which events are mutually exclusive, shall we?

Choosing a card that is an ace and a four: This seems like a rather tricky combination, my friend. Unfortunately, I'm pretty sure this event is impossible because a card can't be both an ace and a four at the same time. So, no, this one is not mutually exclusive.

Choosing a card that is a diamond and a king: Ah, the royal diamond! Well, since there is only one king of diamonds in a standard deck, this event is indeed mutually exclusive. You can either choose a king or a diamond, but not both at the same time. So, yes, this one is mutually exclusive.

Choosing a card that is a king and a heart: Now, the combination of a king and a heart seems like a fun one! However, even though there is only one king of hearts in a standard deck, this event is not mutually exclusive. One card can definitely be both a king and a heart, so it is possible for this event to occur. So, no, this one is not mutually exclusive.

Choosing a card that is a king and a queen: Ah, the royal couple! While there is only one king of each suit in a standard deck, you can indeed choose both a king and a queen at the same time. So, this event is not mutually exclusive.

Choosing a card that is a heart and an odd number: A hearty odd number, you say? Well, here's the deal. There are odd-numbered cards in multiple suits, including hearts. So, it is possible to choose a card that is both a heart and an odd number. Thus, this event is not mutually exclusive either.

So, my friend, the only event that is mutually exclusive is choosing a card that is a diamond and a king. The rest of them don't fit the bill. Keep on dealing and playing with those cards, and may the odds be ever in your favor!

The mutually exclusive events among the given choices are:

1. Choosing a card that is an ace and a four - These two cards cannot be chosen simultaneously as they are different cards.

2. Choosing a card that is a diamond and a king - These two cards also cannot be chosen simultaneously as they are different suits.

3. Choosing a card that is a heart and an odd number - These two events can occur separately since there are odd-numbered cards in the heart suit.

Therefore, the mutually exclusive events are:

- Choosing a card that is an ace and a four
- Choosing a card that is a diamond and a king

To determine which events are mutually exclusive, we need to identify events that cannot occur at the same time. In other words, if one event happens, the other event cannot happen simultaneously.

Let's analyze each option:

1. Choosing a card that is an ace and a four: It is not possible to choose a card that is both an ace and a four at the same time, so these events are mutually exclusive.

2. Choosing a card that is a diamond and a king: It is not possible to choose a card that is simultaneously a diamond and a king, so these events are mutually exclusive.

3. Choosing a card that is a king and a heart: It is possible to choose a card that is both a king and a heart (the king of hearts), so these events are not mutually exclusive.

4. Choosing a card that is a king and a queen: It is not possible to choose a card that is both a king and a queen at the same time, so these events are mutually exclusive.

5. Choosing a card that is a heart and an odd number: It is possible to choose a card that is both a heart and an odd number (e.g., the three of hearts), so these events are not mutually exclusive.

Based on our analysis, the mutually exclusive events are:
- Choosing a card that is an ace and a four.
- Choosing a card that is a diamond and a king.
- Choosing a card that is a king and a queen.

Therefore, the correct answers are:
- Choosing a card that is an ace and a four.
- Choosing a card that is a diamond and a king.
- Choosing a card that is a king and a queen.

Prob(a card that is an ace and a four) = 0 , a card can't be an ace and a four

Prob(a card that is a diamond and a king = 1/52, there is only 1 king of diamonds
next two are easy

prob(a card that is a heart and an odd number) = ...
How many odd hearts are there???