# Lesson Worksheet: Experimental Probability Mathematics

In this worksheet, we will practice interpreting a data set by finding and evaluating experimental probability.

Q1:

The table shows the music preferences of a group of men and women.

Calculate the relative frequency of a randomly selected person being a woman who prefers country music. If necessary, round your answer to 3 decimal places.

Calculate the relative frequency of a randomly selected woman preferring rock music. If necessary, round your answer to 3 decimal places.

Q2:

In probability, what is an experiment defined as?

• Athe set of all possible outcomes of an activity
• Ba repeatable process, or activity, with a number of possible outcomes
• Ca collection of one or more possible outcomes from an activity, which can be described as having certain characteristics

Q3:

James has bought a tetrahedral die that has the values 1 to 4 on its faces. He wants to investigate whether the die is fair, so he decides to roll it 100 times and record all the values in a table. He gets the following results.

 1 2 3 4 23 27 22 28

What is the theoretical probability of rolling a 2, assuming that the die is fair?

• A
• B
• C
• D

What is Jamesβs experimental probability for rolling a 2?

• A
• B
• C
• D

Does the difference in these two probabilities mean that the die is most likely to be biased or unbiased?

• ABiased
• BUnbiased

Q4:

A six-sided die with the numbers 1β6 was rolled 42 times, and the number on the upper face was recorded in the table. What is the probability of getting a 5?

 The Number on The Upper Face Frequency 1 2 3 4 5 6 10 5 9 5 10 3
• A
• B
• C
• D

Q5:

A light bulb manufacturer examined a sample of 1,000 light bulbs from their production. Using the table which shows the results for this sample, calculate the experimental probability that a light bulb fails after less than 150 hours of use.

 π» (Hours of Use) Number of Lamps π»<150 150β€π»<400 400β€π»<1,000 π»β₯1,000 150 320 270 260
• A
• B
• C
• D
• E

Q6:

Chloe wants to compare theoretical and experimental probabilities. She decides to roll a die 12 times, 120 times, and 1,200 times and then compare the three distributions.

After 12 rolls, she got the following results:

 1 2 3 4 5 6 2 1 0 2 2 5

After 120 rolls, she got the following results:

 1 2 3 4 5 6 23 18 35 13 15 16

After 1,200 rolls, she got the following results:

 1 2 3 4 5 6 208 196 211 191 200 194

Chloe knows that the theoretical probability of rolling a 3 is , correct to three decimal places.

Using the experiment with 12 trials, calculate the experimental probability of rolling a 3.

Using the experiment with 120 trials, calculate the experimental probability of rolling a 3. Give your answer as a decimal to three decimal places.

Using the experiment with 1,200 trials, calculate the experimental probability of rolling a 3. Give your answer as a decimal to three decimal places.

If Chloe were to continue rolling her dice and record 12,000 rolls, would you anticipate that the experimental probability for rolling a 3 would get closer to or further away from the theoretical probability?

• ACloser to it
• BFurther away from it

Q7:

A life insurance company used a sample of 4,000 men between the ages of 50 and 60 to find the probability of a man dying between these ages. Given that 17 men in the sample died, calculate the experimental probability that a man between the ages of 50 and 60 would die.

Q8:

A company that manufactures light bulbs tests a sample of 1,000 light bulbs to determine their lifespan. The results are shown in the table. What is the probability that a light bulb lasts at least 400 hours?

 π» (Maximum Working Hours) Number of Lamps Less than 150 150β€π»<400 400β€π»<1,000 More than 1,000 100 320 270 310
• A
• B
• C
• D
• E

Q9:

A factory produces two types of televisions and wants to decide how many of each to produce. The table shows the sales of a sample of 50 TV sets from each of 5 malls. If the factory is going to produce 6,000 TV sets in total, how many should be of type B?

 Mall Sales of Type A Sales of Type B 1 2 3 4 5 16 36 34 14 15 34 14 16 36 35

Q10:

A sample of 64 people found that 36 of them watch Channel A, 29 of them watch Channel B, and 11 watch both channels. What is the probability that a random person from the sample only watches Channel A?

• A
• B
• C
• D
• E

This lesson includes 19 additional questions and 225 additional question variations for subscribers.