Math worksheet featuring questions on theoretical and experimental probability, including a frequency table for rolling a number cube.

Let’s go through each question one by one, step by step. We’ll use the table provided to answer experimental probability questions, and basic math for theoretical ones.

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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?

From the table:

- Number 2 (even) → frequency 3
- Number 4 (even) → frequency 6
- Number 6 (even) → frequency 6

Total even rolls = 3 + 6 + 6 = 15

Total rolls overall = add all frequencies:
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

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 of times = 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: under “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 → that’s 2 outcomes.
Total possible = 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:

- Number 5 → frequency 4
- Number 6 → frequency 6
Total = 4 + 6 = 10

Total rolls = 36 (from earlier)

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 knowing a coin has a 50% chance of heads.
Experimental probability is what *actually* happened when you did the experiment — like flipping a coin 10 times and getting 7 heads.

They can be different because experiments have randomness. The more trials you do, the closer experimental usually gets to theoretical.

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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 is what should happen based on math; experimental is what actually happened in the test.
8.) 28