Certainly! Let’s solve the “Dice Probability” worksheet step by step.
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##
Section A: Basic Dice Facts
1) How many faces are there on a normal dice?
✔ Answer: 6
A standard die (singular of dice) is a cube with 6 faces, numbered 1 through 6.
2) What are the possible scores on a normal dice?
✔ Answer: 1, 2, 3, 4, 5, 6
These are the numbers that can appear when you roll a fair six-sided die.
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##
Section B: Probability Calculations (Simplified Fractions)
We assume a
fair six-sided die, so each outcome (1–6) has equal probability:
→ Total outcomes = 6
→ Probability of any single outcome = 1/6
Let’s go one by one:
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1) P(1) → Probability of rolling a 1
✔ Answer: 1/6
2) P(3) → Probability of rolling a 3
✔ Answer: 1/6
3) P(5) → Probability of rolling a 5
✔ Answer: 1/6
4) P(6) → Probability of rolling a 6
✔ Answer: 1/6
5) P(8) → Probability of rolling an 8
→ But a die only goes up to 6 → Impossible event
✔ Answer: 0
6) P(1 or 2) → Rolling a 1 or a 2
→ Favorable outcomes: {1, 2} → 2 outcomes
✔ Answer: 2/6 = 1/3
7) P(3 or 5) → Rolling a 3 or 5
→ Favorable outcomes: {3, 5} → 2 outcomes
✔ Answer: 2/6 = 1/3
8) P(4, 5 or 6) → Rolling 4, 5, or 6
→ Favorable outcomes: {4,5,6} → 3 outcomes
✔ Answer: 3/6 = 1/2
9) P(1, 2, 3 or 4) → Rolling 1,2,3, or 4
→ Favorable outcomes: {1,2,3,4} → 4 outcomes
✔ Answer: 4/6 = 2/3
10) P(not a 6) → Rolling anything except 6
→ Favorable outcomes: {1,2,3,4,5} → 5 outcomes
✔ Answer: 5/6
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11) P(odd) → Odd numbers on die: 1, 3, 5 → 3 outcomes
✔ Answer: 3/6 = 1/2
12) P(multiple of 2) → Even numbers: 2, 4, 6 → 3 outcomes
✔ Answer: 3/6 = 1/2
13) P(multiple of 3) → Multiples of 3: 3, 6 → 2 outcomes
✔ Answer: 2/6 = 1/3
14) P(greater than 1) → Numbers >1: 2,3,4,5,6 → 5 outcomes
✔ Answer: 5/6
15) P(less than 3) → Numbers <3: 1,2 → 2 outcomes
✔ Answer: 2/6 = 1/3
16) P(factor of 12)
→ Factors of 12 within 1–6: 1,2,3,4,6 → (since 1×12, 2×6, 3×4) → 5 outcomes
✔ Answer: 5/6
17) P(factor of 20)
→ Factors of 20 within 1–6: 1,2,4,5 → (since 20=1×20, 2×10, 4×5) → 4 outcomes
✔ Answer: 4/6 = 2/3
18) P(factor of 36 ≥ 3)
→ Factors of 36: 1,2,3,4,6,9,12,18,36
→ Within 1–6 and ≥3: 3,4,6 → 3 outcomes
✔ Answer: 3/6 = 1/2
19) P(prime number)
→ Prime numbers between 1–6: 2,3,5 → (Note: 1 is not prime) → 3 outcomes
✔ Answer: 3/6 = 1/2
20) P(square number)
→ Square numbers between 1–6: 1 (1²), 4 (2²) → 2 outcomes
✔ Answer: 2/6 = 1/3
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##
Section C: Plotting Events on a Probability Scale
We have a number line from 0 to 1. We need to place these events:
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A: A score of 5 → P = 1/6 ≈ 0.167 → Place near left end
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B: Not a score of 5 → P = 5/6 ≈ 0.833 → Place near right end
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C: A score ≤ 5 → P = 5/6 ≈ 0.833 → Same as B
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D: An odd prime number → Odd primes: 3,5 → P = 2/6 = 1/3 ≈ 0.333 → Middle-left
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E: A triangle number → Triangle numbers ≤6: 1, 3, 6 → P = 3/6 = 1/2 → Center
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F: Not a square number → Square numbers: 1,4 → Not squares: 2,3,5,6 → P = 4/6 = 2/3 ≈ 0.667 → Right of center
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✔ Final Placement on Number Line (0 to 1):
```
0 1/6 1/3 1/2 2/3 5/6 1
|------|-------|-------|-------|-------|--------|
A D E F B,C
```
> Note: B and C both have probability 5/6 → same position.
> D = 1/3, E = 1/2, F = 2/3, A = 1/6
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## 🎯 Summary of All Answers:
Section A:
1) 6
2) 1, 2, 3, 4, 5, 6
Section B:
1) 1/6
2) 1/6
3) 1/6
4) 1/6
5) 0
6) 1/3
7) 1/3
8) 1/2
9) 2/3
10) 5/6
11) 1/2
12) 1/2
13) 1/3
14) 5/6
15) 1/3
16) 5/6
17) 2/3
18) 1/2
19) 1/2
20) 1/3
Section C:
Place on scale:
- A → 1/6
- B & C → 5/6
- D → 1/3
- E → 1/2
- F → 2/3
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✔ You’re all set! This covers every question on the worksheet with clear explanations. Let me know if you’d like a visual diagram for Section C too!
Parent Tip: Review the logic above to help your child master the concept of probability of numbers worksheet.
