Let’s go through each question one by one, step by step.
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1.) What is the theoretical probability that an even number will be rolled on a number cube?
A standard number cube has 6 sides: 1, 2, 3, 4, 5, 6.
Even numbers are: 2, 4, 6 → that’s 3 out of 6.
So, theoretical probability = 3/6 =
1/2
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2.) What was the experimental probability of how many times an even number was actually rolled using the table?
First, add up all the frequencies to get total rolls:
8 (for 1) + 3 (for 2) + 9 (for 3) + 6 (for 4) + 4 (for 5) + 6 (for 6) =
8+3=11; 11+9=20; 20+6=26; 26+4=30; 30+6=
36 total rolls
Now, even numbers are 2, 4, 6. Their frequencies:
2 → 3 times
4 → 6 times
6 → 6 times
Total even rolls = 3 + 6 + 6 =
15
Experimental probability = 15 / 36 → simplify: divide numerator and denominator by 3 →
5/12
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3.) If you roll a number cube 36 times, how many times would you expect to roll the number one?
Theoretical probability of rolling a 1 is 1/6.
Expected number = 36 × (1/6) =
6 times
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4.) How many times did you actually roll the number one in the experiment?
Look at the table: for “Number on Cube” = 1, Frequency =
8
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5.) What is the theoretical probability for rolling a number greater than 4?
Numbers greater than 4 on a cube: 5 and 6 → 2 outcomes
Total possible outcomes: 6
Probability = 2/6 =
1/3
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6.) What was the experimental probability of rolling a number greater than 4?
From table:
5 → frequency 4
6 → frequency 6
Total = 4 + 6 =
10
Total rolls = 36 (from Q2)
Experimental probability = 10/36 → simplify: divide by 2 →
5/18
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7.) What is the difference between theoretical and experimental probability?
Theoretical probability is what *should* happen based on math — like expecting 1/2 chance for even numbers.
Experimental probability is what *actually* happened when you did the experiment — like getting 15 evens out of 36 rolls (which is 5/12).
They’re often close, but not always exactly the same — especially with small experiments.
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8.) If a car factory checks 360 cars and 8 of them have defects, how many will have defects out of 1260?
This is a proportion problem.
Defect rate = 8 / 360
We want to find how many defects in 1260 cars:
Set up: (8 / 360) = x / 1260
Cross-multiply:
8 × 1260 = 360 × x
10080 = 360x
Divide both sides by 360:
x = 10080 ÷ 360
Let’s calculate:
360 × 28 = 10080 → so x =
28
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Final Answer:
1.) 1/2
2.) 5/12
3.) 6
4.) 8
5.) 1/3
6.) 5/18
7.) Theoretical probability is what should happen based on math; experimental probability is what actually happened in the experiment.
8.) 28
Parent Tip: Review the logic above to help your child master the concept of experimental probability worksheet.
