Pick a card: the chance of one event
Shuffle a pack of 52 playing cards and draw one. Find the probability of a red card, a king, a face card or the ace of spades, and draw many times to see how often each really comes up.
Core concept
Probability = number of favourable cards ÷ 52, and P(not E) = 1 − P(E)
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. When the pack is shuffled well, every card is equally likely to be drawn. So the probability: How likely something is to happen, from 0 (impossible) to 1 (certain). All key words of an event is the number of cards that give it (the favourable cards) divided by 52. A probability is always between 0 (impossible) and 1 (certain). An event and its opposite always add up to 1: P(not E) = 1 − P(E).
What you will learn
- Count the favourable cards for an event and find its probability out of 52.
- Use P(not E) = 1 − P(E).
- Compare the share seen in many draws with the probability worked out.
Before you start
- Write a fraction in its lowest terms and as a decimal.
Materials
- A pack of 52 playing cards (jokers taken out)
Equipment
- A table to shuffle and lay out the cards
Procedure
- Choose an event, count its favourable cards and work out its probability.
- Try red, a king, a face card and a card that is not a heart.
- Draw a card many times, putting it back each time, and compare the share of kings with the probability.
How this simulation is simplified
- The pack has 52 cards and no jokers, and it is shuffled so every card is equally likely.
- In the draws, the card is put back and the pack shuffled again each time.