1. Total discs: 4 purple (P), 5 white (W), 2 black (B) → 11 discs total.
2. First draw: 11 discs, second draw: 10 discs (since not replaced).
3. Tree diagram:
- First branch: P (4/11), W (5/11), B (2/11)
- From each first draw, second draw probabilities adjust.
4. Complete the tree diagram:
- P → P: (4/11) × (3/10) = 12/110
- P → W: (4/11) × (5/10) = 20/110
- P → B: (4/11) × (2/10) = 8/110
- W → P: (5/11) × (4/10) = 20/110
- W → W: (5/11) × (4/10) = 20/110
- W → B: (5/11) × (2/10) = 10/110
- B → P: (2/11) × (4/10) = 8/110
- B → W: (2/11) × (5/10) = 10/110
- B → B: (2/11) × (1/10) = 2/110
5. a. Use the tree diagram:
i. One purple one white: P→W + W→P = 20/110 + 20/110 = 40/110 = 4/11
ii. One black one white: W→B + B→W = 10/110 + 10/110 = 20/110 = 2/11
iii. The same color: P→P + W→W + B→B = 12/110 + 20/110 + 2/110 = 34/110 = 17/55
Parent Tip: Review the logic above to help your child master the concept of probability trees worksheet.
