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

# 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 Jamesβs 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 1β6 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 |
---|---|---|---|---|---|---|

Frequency | 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.

(Hours of Use) | ||||
---|---|---|---|---|

Number of Lamps | 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?

(Maximum Working Hours) | Less than 150 | More than 1,000 | ||
---|---|---|---|---|

Number of Lamps | 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 | 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?

- A
- B
- C
- D
- E