Probability Worksheets | Dynamically Created Probability Worksheets - Free Printable

Let’s go through each question one by one. We’re working with a standard six-sided die, which has faces numbered:
1, 2, 3, 4, 5, 6

That means there are 6 possible outcomes, and each is equally likely.

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1) Find the probability of rolling a 4 or smaller.

Numbers that are 4 or smaller: 1, 2, 3, 4 → that’s 4 numbers

Probability = favorable outcomes / total outcomes = 4/6 = 2/3

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2) Find the probability of rolling factors of 12.

Factors of 12: numbers that divide 12 evenly.

Check which of 1–6 divide 12:

- 1 → yes (12 ÷ 1 = 12)
- 2 → yes (12 ÷ 2 = 6)
- 3 → yes (12 ÷ 3 = 4)
- 4 → yes (12 ÷ 4 = 3)
- 5 → no (12 ÷ 5 = 2.4 → not whole)
- 6 → yes (12 ÷ 6 = 2)

So factors of 12 on a die: 1, 2, 3, 4, 6 → 5 numbers

Probability = 5/6

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3) Find the probability of rolling a divisor of 30.

Divisors of 30: numbers that divide 30 evenly.

Check 1–6:

- 1 → yes
- 2 → yes (30 ÷ 2 = 15)
- 3 → yes (30 ÷ 3 = 10)
- 4 → no (30 ÷ 4 = 7.5)
- 5 → yes (30 ÷ 5 = 6)
- 6 → yes (30 ÷ 6 = 5)

So divisors: 1, 2, 3, 5, 6 → 5 numbers

Probability = 5/6

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4) List all possible outcomes from rolling a die.

This is just listing what can come up:
1, 2, 3, 4, 5, 6

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5) Find the probability of rolling less than a 4.

Less than 4: 1, 2, 3 → 3 numbers

Probability = 3/6 = 1/2

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6) Find the probability of rolling a divisor of 12.

Wait — this is the same as question #2! Divisors of 12 are the same as factors of 12.

We already did this: 1, 2, 3, 4, 6 → 5 numbers

Probability = 5/6

*(Note: “divisor” and “factor” mean the same thing here.)*

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7) Find the probability of rolling an even prime number.

Prime numbers: only divisible by 1 and itself.

Primes between 1–6: 2, 3, 5

Even primes: only 2 is even and prime.

So only 1 outcome: 2

Probability = 1/6

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8) Find the probability of rolling a divisor of 20.

Divisors of 20: check 1–6

- 1 → yes
- 2 → yes (20 ÷ 2 = 10)
- 3 → no (20 ÷ 3 ≈ 6.66)
- 4 → yes (20 ÷ 4 = 5)
- 5 → yes (20 ÷ 5 = 4)
- 6 → no (20 ÷ 6 ≈ 3.33)

So divisors: 1, 2, 4, 5 → 4 numbers

Probability = 4/6 = 2/3

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9) Find the probability of rolling factors of 20.

Same as above — factors = divisors.

Still: 1, 2, 4, 5 → 4 numbers

Probability = 4/6 = 2/3

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10) Find the probability of rolling factors of 120.

Factors of 120: we need to see which of 1–6 divide 120.

But since 120 is big, let’s check:

- 1 → yes
- 2 → yes
- 3 → yes (1+2+0=3 → divisible by 3)
- 4 → yes (last two digits 20 ÷ 4 = 5)
- 5 → yes (ends in 0)
- 6 → yes (divisible by 2 and 3)

ALL numbers 1–6 divide 120!

So favorable outcomes: 6

Probability = 6/6 = 1

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Final Answer:

1) 2/3
2) 5/6
3) 5/6
4) 1, 2, 3, 4, 5, 6
5) 1/2
6) 5/6
7) 1/6
8) 2/3
9) 2/3
10) 1