Probability Trees – Conditional – Relay Race In this competitive activity students work in teams to answer questions provided on small pieces of paper. Students should check their answers with the teacher (who can be anywhere in the room with their answer sheet). If students are correct they can collect the next numbered sheet (easily placed in piles face-up on a desk at the front). If students are wrong they can skip the question or be given 1 or more chances.

Printing To print handouts from slides - Select the slide from the left. Then click: File > Print > ‘Print Current Slide’ To print multiple slides - Click on a section title to highlight all those slides, or press ‘Ctrl’ at the same time as selecting slides to highlight more than one. Then click: File > Print > ‘Print Selection’ To print double-sided handouts - Highlight both slides before using ‘Print Selection’. Choose ‘Print on Both Sides’ and ‘Flip on Short Edge’.

Relay Race! Conditional Probability Trees

1 10 cubes are in a bag: 4 red and 6 yellow. Two cubes are picked at random. What is the probability both cubes are red? 2 7 green and 3 blue cubes are in a box. Two cubes are picked at random. What is the probability both cubes are green? RR RY YR YY R Y 4 10 6 10 5 9 4 9 6 9 3 9 GG GB BG BB G B 3 The probability a team wins their first match is 0.4. If they win, the probability of winning their second match is 0.6. If they lose, the probability of winning their second match is 0.3. What is P(Win then Lose)? 4 The probability a student passes the first maths test is 0.8. If they pass, the probability of passing the second test is 0.9. If they fail, the probability of passing the second test is 0.5. What is P(FF)? CTRL-Left Click slides to select. Go to Print > ‘Print Selection’ and choose the amount of copies you need (one per team).

5 6 7 8 6 black and 5 yellow pens are in a box. Two pens are picked at random. What is the probability at least one of the pens is black? 6 P(Rain tomorrow) = 4/7. If it rains, the probability of it raining the next day is 2/3. If it doesn’t rain, that probability changes to 1/3. What is the probability it rains on at least one of the days? 7 In a group, 5 students have blonde hair, 3 have black hair and 2 have red hair. What is the probability the teacher randomly picks three students who all have blonde hair? 8 A bag contains 3 blue buttons, 2 green buttons and 2 white buttons. Two buttons are picked randomly. What is P(same colour)?

Teacher’s Answer Sheet

1 10 cubes are in a bag: 4 red and 6 yellow. Two cubes are picked at random. What is the probability both cubes are red? 12 90 2 7 green and 3 blue cubes are in a box. Two cubes are picked at random. What is the probability both cubes are green? 42 90 4 10 × 3 9 = 12 90 RR 4 10 × 6 9 = 24 90 RY 6 10 × 4 9 = 24 90 YR 6 10 × 5 9 = 30 90 YY R Y 4 10 6 10 5 9 4 9 6 9 3 9 7 10 × 6 9 = 42 90 GG 7 10 × 3 9 = 21 90 GB 3 10 × 7 9 = 21 90 BG 3 10 × 2 9 = 6 90 BB G B 7 10 3 10 2 9 7 9 3 9 6 9 3 The probability a team wins their first match is 0.4. If they win, the probability of winning their second match is 0.6. If they lose, the probability of winning their second match is 0.3. What is P(Win then Lose)? 4 The probability a student passes the first maths test is 0.8. If they pass, the probability of passing the second test is 0.9. If they fail, the probability of passing the second test is 0.5. What is P(FF)? 0.16 0.1 0.6 WW 0.4×0.6=0.24 0.9 PP 0.8×0.9=0.72 CTRL-Left Click slides to select. Go to Print > ‘Print Selection’ and choose the amount of copies you need (one per team). 0.4 W 0.8 P 0.4 WL 0.4×0.4=0.16 0.1 PF 0.8×0.1=0.08 0.3 LW 0.6×0.3=0.18 0.5 FP 0.2×0.5=0.1 0.6 0.2 L F 0.7 LL 0.6×0.7=0.42 0.5 FF 0.2×0.5=0.1

5 6 black and 5 yellow pens are in a box. Two pens are picked at random. What is the probability at least one of the pens is black? 90 110 6 P(Rain tomorrow) = 4/7. If it rains, the probability of it raining the next day is 2/3. If it doesn’t rain, that probability changes to 1/3. What is the probability it rains on at least one of the days? 15 21 6 11 × 5 10 = 30 110 BB BY 5 11 × 6 10 = 30 110 YB 5 11 × 4 10 = 20 110 YY B Y 6 11 5 11 4 10 6 10 5 10 4 7 × 2 3 = 8 21 RR 4 7 × 1 3 = 4 21 RX 3 7 × 1 3 = 3 21 XR 3 7 × 2 3 = 6 21 XX R X 4 7 3 7 2 3 1 3 7 In a group, 5 students have blonde hair, 3 have black hair and 2 have red hair. What is the probability the teacher randomly picks three students who all have blonde hair? 60 720 8 A bag contains 3 blue buttons, 2 green buttons and 2 white buttons. Two buttons are picked randomly. What is P(same colour)? 10 42 2 6 B 3 7 3 7 × 2 6 = 6 42 G BB B W 2 7 5 10 4 9 3 8 B BL BL BL 1 6 G G 2 7 × 1 6 = 2 42 GG 5 10 × 4 9 × 3 8 = 60 720 W 2 7 B W 2 7 × 1 6 = 2 42 G 1 6 WW W

tom@goteachmaths.co.uk Questions? Comments? Suggestions? …or have you found a mistake!? Any feedback would be appreciated . Please feel free to email: tom@goteachmaths.co.uk