Learning objectives

1. Learning objectives • To be able to calculate probabilities for combinations of experiments by using sample space diagrams (level 6) • To learn to justify solutions and predictions with the help of diagrams (level 7) • To calculate probabilities of combinations of experiments by using the AND and OR rule (extension task) (level 8)

2. First spinner Second spinner Starter: 2 3 2 2 3 1 Discuss with the person sitting next to you (use the back of your exercise book for any rough work): If you spin both spinners and add the results: 1) What different totals can you get? 2) Are all the totals equally likely? 3) What will happen if you spin the spinners 100 times?

3. 2 3 Starter: 2 2 3 Second spinner 1 First spinner 3) What will happen if you spin the spinners 100 times?

4. There are 5 pens in a pack (1 red, 1 orange, 1 mud-brown and 2 black).I take a pen at random, look at it, return it then take another pen at random. What is the probability that both the pens I take are the same colour?

5. Sample space diagram Second pen P( 1st black)= P(2nd black) = P(1st black AND 2nd black)= P(same)= First pen

6. What if we use this as a game of chance at the Summer Fair? Second pen P(same)= What if I charge 20p a go and give £1 prize if players pick two pens the same colour? First pen I know that 100 people will play – how much should I charge to make at least £20 profit? (keep to £1 prize)

7. Summer Fair – Designing a Game of Chance Follow the ground rules for working in groups. Try to earn as many points as possible (see task sheet) Homework: (Due next Wednesday – joint presentation) Complete the Summer Fair task – make sure you test your game and record what happens. Ext: research and include the AND and OR rules