Tree Diagrams – Mixed – 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! Tree Diagrams

1 2 3 4 4 10 6 10 300 students are in Year 10. 120 are male. 80 males take History. 60 females do not take History. Complete the frequency tree. 2 280 students are in Year 9. 160 are female. 90 females take Art. 70 males do not take Art. Complete a frequency tree with this info. From the females, what is P(take History)? From everyone, what is P(does not take Art)? take History male do not take History take History female do not take History 10 cubes are in a bag: 4 red and 6 yellow. A cube is picked and replaced, then another cube is picked. Complete the tree diagram. What is the probability both cubes are red? 3 4 6 green and 3 blue cubes are in a box. A cube is picked and replaced, then another cube is picked. Complete a tree diagram. What is the probability only one of the cubes is green? RR 4 10 R CTRL-Left Click slides to select. Go to Print > ‘Print Selection’ and choose the amount of copies you need (one per team). RY 6 10

5 6 7 8 0.6 0.4 0.4 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(Lose then Win)? 6 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(Pass one or more)? 0.6 WW 0.4 W 0.4 L 7 7 black and 4 yellow pens are in a box. Two pens are picked at random. What is the probability at least one of the pens is yellow? 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

1 300 students are in Year 10. 120 are male. 80 males take History. 60 females do not take History. Complete the frequency tree. 2 3 2 280 students are in Year 9. 160 are female. 90 females take Art. 70 males do not take Art. Complete a frequency tree with this info. 1 2 From the females, what is P(take History)? From everyone, what is P(does not take Art)? take History 80 take Art 50 120 120 male male 40 70 do not take History do not take Art take History 120 take Art 90 female 180 female 160 60 70 do not take History do not take Art 10 cubes are in a bag: 4 red and 6 yellow. A cube is picked and replaced, then another cube is picked. Complete the tree diagram. What is the probability both cubes are red? 3 16 100 = 4 25 4 6 green and 3 blue cubes are in a box. A cube is picked and replaced, then another cube is picked. Complete a tree diagram. What is the probability only one of the cubes is green? 36 81 = 4 9 4 10 4 10 × 4 10 = 16 100 6 9 × 6 9 = 36 81 GG 3 9 × 3 9 = 18 81 GB 3 9 × 6 9 = 18 81 BG 3 9 × 3 9 = 9 81 BB G B 6 9 3 9 RR 4 10 R CTRL-Left Click slides to select. Go to Print > ‘Print Selection’ and choose the amount of copies you need (one per team). 4 10 × 6 10 = 24 100 6 10 RY 4 10 6 10 × 4 10 = 24 100 YR 6 10 Y 6 10 × 6 10 = 36 100 6 10 YY

5 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(Lose then Win)? 6 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(Pass one or more)? 0.18 0.9 0.6 WW 0.4×0.6=0.24 0.9 PP 0.8×0.9=0.72 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 7 7 black and 4 yellow pens are in a box. Two pens are picked at random. What is the probability at least one of the pens is yellow? 68 110 = 34 55 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 = 5 21 2 6 B 7 11 × 6 10 = 42 110 BB 7 11 × 4 10 = 28 110 BY 4 11 × 7 10 = 28 110 YB 4 11 × 3 10 = 12 110 YY B Y 7 11 4 11 3 10 7 10 4 10 6 10 3 7 3 7 × 2 6 = 6 42 G BB B W 2 7 B 1 6 G G 2 7 × 1 6 = 2 42 GG 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