In probability, there's a very important distinction between the words and and or.

• And means that the outcome has to satisfy both conditions at the same time.
• Or means that the outcome has to satisfy one condition, or the other condition, or both at the same time.

Let's look at one probability in these two ways:

AND Probability

What is the probability of drawing a card from a deck and it being red and a face card?

For this probability, we need to look at which cards are both red and face cards. There are 6 of these: Jack of Hearts, Queen of Hearts, King of Hearts, Jack of Diamonds, Queen of Diamonds, and King of Diamonds.

OR Probability

What is the probability of drawing a card from a deck and it being red or a face card?

This time the card can be red, or a face card, or both at the same time. There are 26 red cards (6 of which are also face cards). In addition, there are 6 more face cards that are not red: Jack of Clubs, Queen of Clubs, King of Clubs, Jack of Spades, Queen of Spades, and King of Spades. That is a total of 26 + 6 = 32 cards.

Be careful not to just add up the number of face cards (12) with the number of red cards (26). That would give a total of 38 cards, but it would count the red face cards twice.

Notice how much these two probabilities differ. One little word changes the whole problem!

And Vs. Or Probability Practice: