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.

1234
23272228

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

  • A14
  • B16
  • C12
  • D15

What is James’s experimental probability for rolling a 2?

  • A27100
  • B22100
  • C16
  • D14

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 1–6 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 Face123456
Frequency 10 5 9 5 10 3
  • A314
  • B521
  • C542
  • D114

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.

𝐻 (Hours of Use)𝐻<150150≀𝐻<400400≀𝐻<1,000𝐻β‰₯1,000
Number of Lamps 150 320 270 260
  • A320
  • B27100
  • C825
  • D47100
  • E1720

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:

123456
210225

After 120 rolls, she got the following results:

123456
231835131516

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

123456
208196211191200194

Chloe knows that the theoretical probability of rolling a 3 is 16=0.167, 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?

𝐻 (Maximum Working Hours)Less than 150150≀𝐻<400400≀𝐻<1,000More than 1,000
Number of Lamps 100 320 270 310
  • A2950
  • B2150
  • C31100
  • D910
  • E27100

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

  • A932
  • B916
  • C2964
  • D2564
  • E2554

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

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