Data and probability · Ages 14–15
Tree diagrams worksheet
Part of: Probability
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Tree diagrams worksheet
Data and probability · Ages 14–15
Numsprite
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Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.A family has 2 children, each as likely a boy (B) as a girl (G), as the tree diagram shows. The tree has outcomes; of them have exactly 0 girls.
Fill in each blank
Answer:
2.Tsz-ching tosses 2 coins, and the tree diagram lists every outcome (H heads, T tails). The probability of exactly 1 heads is .
Answer in simplest form
Answer:
3.A bag holds 6 red balls (R) and 3 blue (B). One is drawn, its colour noted and put back, and another drawn, as the tree shows. The probability that both are red is .
Answer in simplest form
Answer:
4.A bag holds 5 red balls (R) and 1 blue (B). One is drawn and not put back, then another, as the tree shows. The probability that both are red is .
Answer in simplest form
Answer:
5.There are 2 roads from A to B and 3 from B to C. Going from A to C through B, there are different routes; choosing one at random, the probability of Tsz-hin's favourite is .
Fill in each blank
Answer:
6.There are 2 roads from A to B and 5 from B to C. Going from A to C through B, there are different routes; choosing one at random, the probability of Ming's favourite is .
Fill in each blank
Answer:
7.A bag holds 5 red balls (R) and 5 blue (B). One is drawn, its colour noted and put back, and another drawn, as the tree shows. The probability that both are red is .
Answer in simplest form
Answer:
8.A bag holds 6 red balls (R) and 5 blue (B). One is drawn and not put back, then another, as the tree shows. The probability of one red and one blue, in either order, is .
Answer in simplest form
Answer:
9.A bag holds 3 red balls (R) and 4 blue (B). One is drawn and not put back, then another, as the tree shows. The probability of one red and one blue, in either order, is .
Answer in simplest form
Answer:
Part B: Choose, or true or false (2 marks each)
10.A bag holds 7 red balls and 3 blue. A red one is drawn and not put back, then another is drawn. What is the probability the second is red?
- A. 710
- B. 79
- C. 35
- D. 23
Choose the right answer
Answer:
11.Tossing 5 coins, the probability that all land the same way (all heads or all tails) is 116.
True or false?
Answer:
12.Tossing 5 coins, the probability that all land the same way (all heads or all tails) is 132.
True or false?
Answer:
Part C: Word problems (4 marks each)
13.A team wins each match with probability 23, each match unaffected by the others. The probability of winning two in a row is ; of winning neither is .
Fill in each blank
Working:
Answer:
14.A lucky-draw box holds 16 tickets, 3 of them winners. Ka-yan and then Tsz-ching each draw one, without putting it back. What is the probability both win?
Answer in simplest form
Working:
Answer:
15.A pencil case holds 5 red ballpoint pens and 3 blue. May takes two at random, one after the other, without putting any back. What is the probability both are blue?
Answer in simplest form
Working:
Answer:
16.Chi-keung has 6 tops and 4 pairs of trousers; 1 of the tops are white and 3 of the trousers blue. Picking a top and trousers at random, there are outfits; the probability of a white top with blue trousers is .
Fill in each blank
Working:
Answer:
17.Ka-lok tosses 5 coins and starts the game first if at least one lands heads. What is the probability Ka-lok starts first?
Answer in simplest form
Working:
Answer:
18.Chi-keung has 3 tops and 4 pairs of trousers; 1 of the tops are white and 3 of the trousers blue. Picking a top and trousers at random, there are outfits; the probability of a white top with blue trousers is .
Fill in each blank
Working:
Answer:
Show the answers and working
Tree diagrams worksheet: Answers and working
Part A: Working out and filling in
1. 4, 1
Each step splits in 2, so 2 steps make 4 outcomes; those with exactly 0 G number 1.
2. 12
The tree ends in 4 equally likely outcomes, 2 with exactly 1 H: 24 = 12.
3. 49
With the ball put back, both draws are 69; multiply along RR: 69 × 69 = 49.
4. 23
Without replacement: red first 56, then 4 red of 5 left: 56 × 45 = 23.
5. 6, 16
The tree splits into 2, each into 3: 2 × 3 = 6 routes, one of them the favourite: 16.
6. 10, 110
The tree splits into 2, each into 5: 2 × 5 = 10 routes, one of them the favourite: 110.
7. 14
With the ball put back, both draws are 510; multiply along RR: 510 × 510 = 14.
8. 611
Two paths, RB and BR: 611 × 510 + 511 × 610 = 311 + 311 = 611.
9. 47
Two paths, RB and BR: 37 × 46 + 47 × 36 = 27 + 27 = 47.
Part B: Choose, or true or false
10. D. 23
With one red gone, 6 red are left of 9 balls: P = 69.
11. True
The tree has 25 = 32 outcomes, only 2 all the same: 232 = 116.
12. False
The tree has 25 = 32 outcomes, only 2 all the same: 232 = 116.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 49, 19
Multiply along the tree: win-win 23 × 23 = 49; not winning is 13 each, so neither = 19.
14. 140
Ka-yan wins with 316; then 2 winners of 15 are left: 316 × 215 = 140.
15. 328
First blue 38, second blue 27: 38 × 27 = 328.
16. 24, 18
A tree: 6 tops, each splitting into 4 trousers, 24 outfits; white with blue: 1 × 3 = 3, so 324 = 18.
17. 3132
The tree has 32 outcomes and only "all tails" fails: 1 − 132 = 3132.
18. 12, 14
A tree: 3 tops, each splitting into 4 trousers, 12 outfits; white with blue: 1 × 3 = 3, so 312 = 14.
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