Probability with Dice Worksheet | Fun and Engaging 7th Grade PDF ... - Free Printable

Let's solve this step-by-step, starting with each section of the worksheet.

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Section A

1) How many faces are there on a normal dice?
A standard die (plural: dice) is a cube, and a cube has 6 faces.
✔ Answer: 6

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2) What are the possible scores on a normal dice?
The numbers on a standard die range from 1 to 6, so the possible scores are:
✔ Answer: 1, 2, 3, 4, 5, 6

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Section B

We are rolling a fair six-sided die, so each outcome (1 through 6) has an equal probability of $ \frac{1}{6} $. We'll calculate probabilities as simplified fractions.

Let’s go one by one:

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1) P(1)
Only one way to get a 1 → $ \frac{1}{6} $

✔ Answer: $ \frac{1}{6} $

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2) P(3)
Only one way → $ \frac{1}{6} $

✔ Answer: $ \frac{1}{6} $

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3) P(5)
Only one way → $ \frac{1}{6} $

✔ Answer: $ \frac{1}{6} $

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4) P(6)
Only one way → $ \frac{1}{6} $

✔ Answer: $ \frac{1}{6} $

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5) P(8)
8 is not on a die → impossible event

✔ Answer: $ 0 $

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6) P(1 or 2)
Favorable outcomes: 1, 2 → 2 outcomes
$ \frac{2}{6} = \frac{1}{3} $

✔ Answer: $ \frac{1}{3} $

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7) P(3 or 5)
Favorable: 3, 5 → 2 outcomes
$ \frac{2}{6} = \frac{1}{3} $

✔ Answer: $ \frac{1}{3} $

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8) P(4, 5 or 6)
Favorable: 4, 5, 6 → 3 outcomes
$ \frac{3}{6} = \frac{1}{2} $

✔ Answer: $ \frac{1}{2} $

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9) P(1, 2, 3 or 4)
Favorable: 1, 2, 3, 4 → 4 outcomes
$ \frac{4}{6} = \frac{2}{3} $

✔ Answer: $ \frac{2}{3} $

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10) P(not a 6)
Total outcomes: 6
Not a 6 → 1, 2, 3, 4, 5 → 5 outcomes
$ \frac{5}{6} $

✔ Answer: $ \frac{5}{6} $

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11) P(odd)
Odd numbers: 1, 3, 5 → 3 outcomes
$ \frac{3}{6} = \frac{1}{2} $

✔ Answer: $ \frac{1}{2} $

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12) P(multiple of 2)
Multiples of 2: 2, 4, 6 → 3 outcomes
$ \frac{3}{6} = \frac{1}{2} $

✔ Answer: $ \frac{1}{2} $

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13) P(multiple of 3)
Multiples of 3: 3, 6 → 2 outcomes
$ \frac{2}{6} = \frac{1}{3} $

✔ Answer: $ \frac{1}{3} $

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14) P(greater than 1)
Numbers > 1: 2, 3, 4, 5, 6 → 5 outcomes
$ \frac{5}{6} $

✔ Answer: $ \frac{5}{6} $

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15) P(less than 3)
Less than 3: 1, 2 → 2 outcomes
$ \frac{2}{6} = \frac{1}{3} $

✔ Answer: $ \frac{1}{3} $

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16) P(factor of 12)
Factors of 12: 1, 2, 3, 4, 6 (since 12 ÷ 1=12, 12÷2=6, etc.)
From 1–6: 1, 2, 3, 4, 6 → all except 5
So 5 favorable outcomes
$ \frac{5}{6} $

✔ Answer: $ \frac{5}{6} $

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17) P(factor of 20)
Factors of 20: 1, 2, 4, 5, 10, 20
But only values on die: 1, 2, 4, 5 → 4 outcomes
$ \frac{4}{6} = \frac{2}{3} $

✔ Answer: $ \frac{2}{3} $

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18) P(factor of 36 ≥ 3)
First, factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Now pick those ≥ 3 and ≤ 6 (since die only goes up to 6):
→ 3, 4, 6 → 3 outcomes
$ \frac{3}{6} = \frac{1}{2} $

✔ Answer: $ \frac{1}{2} $

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19) P(prime number)
Prime numbers between 1–6: 2, 3, 5
(1 is not prime; 4 = 2×2, 6 = 2×3)
So 3 outcomes
$ \frac{3}{6} = \frac{1}{2} $

✔ Answer: $ \frac{1}{2} $

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20) P(square number)
Square numbers between 1–6:
1 = 1², 4 = 2² → 1 and 4
(9 > 6, so not included)
So 2 outcomes
$ \frac{2}{6} = \frac{1}{3} $

✔ Answer: $ \frac{1}{3} $

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Section C

We need to place events A–F on a probability scale from 0 to 1.

Let’s find the probability of each event and then place it accordingly.

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#### Event A: A score of 3
Only one outcome → $ \frac{1}{6} \approx 0.167 $
➡️ Close to 0

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#### Event B: Not a score of 4
Score of 4: 1 outcome → not 4: 5 outcomes
$ \frac{5}{6} \approx 0.833 $
➡️ Close to 1

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#### Event C: A score ≤ 6
All scores (1–6) are ≤ 6 → certain event
$ \frac{6}{6} = 1 $
➡️ At 1

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#### Event D: An odd prime number
Odd primes on die: 3, 5 (2 is prime but even)
So 2 outcomes → $ \frac{2}{6} = \frac{1}{3} \approx 0.333 $

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#### Event E: A triangle number
Triangle numbers: 1, 3, 6, 10, 15…
On die: 1, 3, 6 → 3 outcomes
$ \frac{3}{6} = \frac{1}{2} = 0.5 $

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#### Event F: Not a square number
Square numbers: 1, 4 → so not square: 2, 3, 5, 6 → 4 outcomes
$ \frac{4}{6} = \frac{2}{3} \approx 0.667 $

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Now let’s order them on the scale:

| Event | Probability | Position |
|-------|-------------|----------|
| A | $ \frac{1}{6} $ ≈ 0.167 | Near 0 |
| D | $ \frac{1}{3} $ ≈ 0.333 | Middle-left |
| E | $ \frac{1}{2} $ = 0.5 | Center |
| F | $ \frac{2}{3} $ ≈ 0.667 | Middle-right |
| B | $ \frac{5}{6} $ ≈ 0.833 | Near 1 |
| C | 1 | At 1 |

So on the line from 0 to 1 (with 5 tick marks), we can assume positions at:

- 0
- 0.2 (≈ 1/5)
- 0.4 (≈ 2/5)
- 0.6 (≈ 3/5)
- 0.8 (≈ 4/5)
- 1

But since it's a simple scale, just place based on relative size.

Final Placement:

- A: Just after 0 → first tick
- D: Second tick (around 0.33)
- E: Third tick (0.5)
- F: Fourth tick (0.67)
- B: Fifth tick (0.83)
- C: At 1

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✔ Summary of Section C:

Place on the scale:

- A → near 0
- D → slightly right of center-left
- E → center
- F → middle-right
- B → near 1
- C → at 1

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✔ Final Answers:

#### Section A
1) 6
2) 1, 2, 3, 4, 5, 6

#### Section B
1) $ \frac{1}{6} $
2) $ \frac{1}{6} $
3) $ \frac{1}{6} $
4) $ \frac{1}{6} $
5) 0
6) $ \frac{1}{3} $
7) $ \frac{1}{3} $
8) $ \frac{1}{2} $
9) $ \frac{2}{3} $
10) $ \frac{5}{6} $
11) $ \frac{1}{2} $
12) $ \frac{1}{2} $
13) $ \frac{1}{3} $
14) $ \frac{5}{6} $
15) $ \frac{1}{3} $
16) $ \frac{5}{6} $
17) $ \frac{2}{3} $
18) $ \frac{1}{2} $
19) $ \frac{1}{2} $
20) $ \frac{1}{3} $

#### Section C
On the probability scale:
- A → close to 0
- D → ~0.33
- E → 0.5
- F → ~0.67
- B → ~0.83
- C → 1

You would place them in increasing order along the line from left to right.

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Let me know if you'd like a visual version of the scale!