This card or that one? The addition rule
Draw one card and win if it is a king or a queen, then a king or a heart. Count the cards that win and find out when you can just add the probabilities and when you must take away the overlap.
Core concept
P(A or B) = P(A) + P(B) − P(A and B); for mutually exclusive events the overlap is 0
Topic: Probability
A pack of playing cards has 52 cards in four suits: spades ♠ and clubs ♣ are black, and hearts ♥ and diamonds ♦ are red. Each suit has 13 cards: the ace, the number cards 2 to 10, and three face cards, the jack, the queen and the king. Sometimes you win if the card is one thing or another: a king or a queen. A card cannot be both a king and a queen, so these events are mutually exclusive, and you can add their probabilities: 4/52 + 4/52. But a card can be both a king and a heart (the king of hearts). If you add 4 kings and 13 hearts you count that card twice, so you take it away once: P(A or B) = P(A) + P(B) − P(A and B).
What you will learn
- Decide whether two events are mutually exclusive.
- Use P(A or B) = P(A) + P(B) for mutually exclusive events.
- Use P(A or B) = P(A) + P(B) − P(A and B) when the events overlap.
Before you start
- Find the probability of a single event when drawing a card.
Materials
- A pack of 52 playing cards (jokers taken out)
Equipment
- A table to lay out the cards in their suits
Procedure
- Choose two events and count the cards in each, and the cards in both.
- Try a king or a queen, and a heart or a spade.
- Try a king or a heart, and a red card or a face card, and take away the overlap.
How this simulation is simplified
- The pack has 52 cards and no jokers, and it is shuffled so every card is equally likely.