Let’s go through each question one by one. Remember, a standard die has 6 sides: numbers 1, 2, 3, 4, 5, and 6. So there are always 6 possible outcomes when you roll it.
Probability = (Number of favorable outcomes) ÷ (Total number of possible outcomes)
Total outcomes = 6
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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 = 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.
From 1 to 6:
1 (yes), 2 (yes), 3 (yes), 4? 12÷4=3 → yes, 5? no, 6? 12÷6=2 → yes.
So factors of 12 on a die: 1, 2, 3, 4, 6 → that’s 5 numbers.
Wait — let me double-check:
12 ÷ 1 = 12 ✔️
12 ÷ 2 = 6 ✔️
12 ÷ 3 = 4 ✔️
12 ÷ 4 = 3 ✔️
12 ÷ 5 = 2.4
✘
12 ÷ 6 = 2 ✔️
Yes, 5 numbers: 1,2,3,4,6
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 to 6:
30 ÷ 1 = 30 ✔️
30 ÷ 2 = 15 ✔️
30 ÷ 3 = 10 ✔️
30 ÷ 4 = 7.5
✘
30 ÷ 5 = 6 ✔️
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.
Just list them: 1, 2, 3, 4, 5, 6
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5) Find the probability of rolling less than a 4.
Less than 4 means: 1, 2, 3 → 3 numbers
Probability = 3/6 =
1/2
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6) Find the probability of rolling a divisor of 12.
This is the same as question #2! Divisors of 12 on a die: 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 (because 3 and 5 are odd)
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 to 6
20 ÷ 1 = 20 ✔️
20 ÷ 2 = 10 ✔️
20 ÷ 3 ≈ 6.66
✘
20 ÷ 4 = 5 ✔️
20 ÷ 5 = 4 ✔️
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.
Factors of 20 on die: 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: any number from 1 to 6 will divide 120? Let’s check:
120 ÷ 1 = 120 ✔️
120 ÷ 2 = 60 ✔️
120 ÷ 3 = 40 ✔️
120 ÷ 4 = 30 ✔️
120 ÷ 5 = 24 ✔️
120 ÷ 6 = 20 ✔️
All 6 numbers work!
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
Parent Tip: Review the logic above to help your child master the concept of probability worksheet 7th grade math.
![Probability Of Compound Events Worksheets [PDF] (7.SP.C.8.A): 7th ...](/images2/probability-worksheet-7th-grade-math/probability-worksheet-7th-grade-math-34.png)
