Lesson 10 of 16
A pack of 52 cards
Show on a big screenYou pick one card from a well-shuffled pack. What is the chance it is a king?
Step 1 of 4
- A pack has 4 suits of 13 cards. That is 52 cards.
- Spades and clubs are black. Hearts and diamonds are red. Each colour has 26 cards.
- Each suit has A, 2 to 10, J, Q and K. The J, Q and K are face cards. There are 12.
- There are 4 kings. P(king) = 4/52 = 1/13.
There are 4 kings in 52 cards. So the chance is 4/52, which is 1/13.
The rule
Shuffling makes every card equally likely. So P = cards that fit ÷ 52.
Count the cards that fit, out of 52.
- Suit — a group of 13 cards: spades, clubs, hearts or diamonds.
- Face cards — the jack, queen and king of each suit. An ace is not one.
- On a card, A is ace and J is jack. Q is queen and K is king.
| Cards | How many |
|---|---|
| The whole pack | 52 |
| One suit | 13 |
| All black cards, or all red | 26 |
| One kind, such as all aces | 4 |
| All face cards | 12 |
| Red face cards | 6 |
Four questions
| Question | Cards that fit | Chance |
|---|---|---|
| a heart | 13 | 13/52 = 1/4 |
| an ace | 4 | 4/52 = 1/13 |
| a red card from 2 to 10 | 18 | 18/52 = 9/26 |
| the 9 of diamonds | 1 | 1/52 |
Red cards from 2 to 10: 9 in each red suit. That is 9 × 2 = 18.
Or. A queen or a heart? Count 4 queens and 13 hearts. That is 17. The queen of hearts is in both lists. It was counted twice. Take 1 away. 16 cards fit. P = 16/52 = 4/13.
Watch out!
Count hearts that are not kings. Do not take all 4 kings from the 13 hearts. Only one king is a heart. Take 1 away. That is 12 cards, not 9.
Now try it. Think about the pack. Tap the right chance.
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Try the lab to finish this lesson.