Experimental Probability exercise - Free Printable

Here are the step-by-step solutions for each question on your worksheet.

1.) What is the theoretical probability that an even number will be rolled on a number cube?
* Step 1: A standard number cube has 6 sides: 1, 2, 3, 4, 5, and 6.
* Step 2: Identify the even numbers. The even numbers are 2, 4, and 6. That is 3 numbers.
* Step 3: The probability is the number of even outcomes divided by the total number of outcomes.
* Probability = $3 / 6$
* Step 4: Simplify the fraction. Both numbers can be divided by 3.
* $3 \div 3 = 1$
* $6 \div 3 = 2$
* Result: $1/2$

2.) What was the experimental probability of how many times an even number was actually rolled using the table?
* Step 1: Find the total number of rolls (trials) by adding up all the frequencies in the table.
* $8 + 3 + 9 + 6 + 4 + 6 = 36$ total rolls.
* Step 2: Find how many times an even number appeared. Look at the rows for 2, 4, and 6.
* Frequency of 2: 3
* Frequency of 4: 6
* Frequency of 6: 6
* Total even rolls = $3 + 6 + 6 = 15$.
* Step 3: Write the experimental probability as a fraction: (Even Rolls) / (Total Rolls).
* Probability = $15 / 36$
* Step 4: Simplify the fraction. Both numbers can be divided by 3.
* $15 \div 3 = 5$
* $36 \div 3 = 12$
* Result: $5/12$

3.) If you roll a number cube 36 times, how many times would you expect to roll the number one?
* Step 1: Find the theoretical probability of rolling a "1". There is only one "1" on a 6-sided cube.
* Probability = $1/6$.
* Step 2: Multiply the probability by the total number of rolls (36) to find the expected value.
* Expected Value = $36 \times (1/6)$
* $36 \div 6 = 6$
* Result: 6 times.

4.) How many times did you actually roll the number one in the experiment?
* Step 1: Look at the frequency table provided in the image.
* Step 2: Find the row for "Number on Cube" equal to 1.
* Step 3: Read the corresponding "Frequency". It is 8.
* Result: 8 times.

5.) What is the theoretical probability for rolling a number greater than 4?
* Step 1: Identify the numbers on a cube that are strictly greater than 4. These are 5 and 6.
* Step 2: Count how many favorable outcomes there are. There are 2 outcomes (5 and 6).
* Step 3: Divide by the total number of sides (6).
* Probability = $2 / 6$
* Step 4: Simplify the fraction by dividing top and bottom by 2.
* Result: $1/3$

6.) What was the experimental probability of rolling a number greater than 4?
* Step 1: Use the total number of rolls calculated in Question 2, which is 36.
* Step 2: Find the frequency of numbers greater than 4 (which are 5 and 6) from the table.
* Frequency of 5: 4
* Frequency of 6: 6
* Total favorable rolls = $4 + 6 = 10$.
* Step 3: Write the probability fraction: $10 / 36$.
* Step 4: Simplify the fraction by dividing top and bottom by 2.
* $10 \div 2 = 5$
* $36 \div 2 = 18$
* Result: $5/18$

7.) What is the difference between theoretical and experimental probability?
* Theoretical Probability: This is what *should* happen based on math and logic. It assumes everything is perfectly fair (like a perfect cube). You calculate this before doing any experiment.
* Experimental Probability: This is what *actually* happened when you performed the test or experiment. It is based on real data collected (like the table in the problem). It might be different from the theoretical probability because of chance.

8.) If a car factory checks 360 cars and 8 of them have defects, how many will have defects out of 1260?
* Step 1: Set up a proportion. The ratio of defective cars should stay the same.
* $\frac{8 \text{ defects}}{360 \text{ cars}} = \frac{x \text{ defects}}{1260 \text{ cars}}$
* Step 2: Solve for $x$. You can cross-multiply or simplify first. Let's simplify the left side first.
* $8 / 360$ simplifies to $1 / 45$ (divide both by 8).
* So, $\frac{1}{45} = \frac{x}{1260}$
* Step 3: Multiply 1260 by $\frac{1}{45}$ (or divide 1260 by 45).
* $1260 \div 45 = 28$
* Result: 28 cars.

Final Answer:
1.) 1/2
2.) 5/12
3.) 6
4.) 8
5.) 1/3
6.) 5/18
7.) Theoretical probability is what is expected to happen based on math, while experimental probability is what actually happens during a real test.
8.) 28