Worksheet on tree diagrams for probability without replacement, designed for GCSE Higher tier students.

Tree Diagrams (B) worksheet from Cazoom Maths, featuring probability problems without replacement, including red and green cubes, boys and girls in a class, and small nails, with tree diagrams to complete.

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Show Answer Key & Explanations Step-by-step solution for: Compound Probability ~ Using Tree Diagrams, Organized Lists and Tables

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- Problem 1:
- a. Probability of two red cubes: (12/18) × (11/17) = 132/306 = 22/51
- b. Probability of at least one green cube: 1 - P(two red) = 1 - 22/51 = 29/51

- Problem 2:
- a. If first is girl, probability second is also girl: 9/29
- b. Probability a girl and boy are chosen: P(B then G) + P(G then B) = (20/30)×(10/29) + (10/30)×(20/29) = 400/870 = 40/87

- Problem 3:
- a. If first nail is too small, probability second is also too small: 4/199
- b. Probability all three nails are too small: (5/200) × (4/199) × (3/198) = 60/7880400 = 1/131340
- c. Probability only the second nail is too small: (195/200) × (5/199) × (194/198) = 189150/7880400 = 1261/52536

Parent Tip: Review the logic above to help your child master the concept of probability tree diagrams worksheets.

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