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Lesson Worksheet: Experimental Probability Mathematics
In this worksheet, we will practice interpreting a data set by finding and evaluating experimental probability.
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.
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
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.
What is the theoretical probability of rolling a 2, assuming that the die is fair?
What is James’s experimental probability for rolling a 2?
Does the difference in these two probabilities mean that the die is most likely to be biased or unbiased?
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 Face||1||2||3||4||5||6|
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.
|(Hours of Use)|
|Number of Lamps||150||320||270||260|
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:
After 120 rolls, she got the following results:
After 1,200 rolls, she got the following results:
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
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.
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?
|(Maximum Working Hours)||Less than 150||More than 1,000|
|Number of Lamps||100||320||270||310|
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?
|Sales of Type A||16||36||34||14||15|
|Sales of Type B||34||14||16||36||35|
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?