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Probability Exploration Worksheet

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Probability Exploration Worksheet

Explore chance using a fair six-sided die. Read the data carefully, show your thinking, and give fractions in their simplest form where possible.

Chance language

Use these terms to describe and investigate chance: outcome, event, trial, theoretical probability and experimental probability.

1.Match each probability term to its definition. Write the correct letter beside each term.

1. Outcome
2. Event
3. Trial
4. Theoretical probability
5. Experimental probability

B. One performance of an experiment
E. The probability calculated from observed results
D. One or more outcomes we are interested in
A. The probability calculated from all equally likely possibilities
C. A result that can happen

2.A fair six-sided die has faces numbered 1 to 6. What is the theoretical probability of rolling a 3? Give your answer as a fraction and a percentage.

3.In 30 rolls of a fair die, how many rolls of a 3 would you expect if the results were exactly in line with the theoretical probability? Show the calculation.

Analyse a class experiment

A group rolled a fair die 60 times and recorded the results below. Use this data for Questions 4–9.

Die face

Number of times rolled

4.Which die face appeared most often, and which appeared least often in the 60 rolls?

5.What was the experimental probability of rolling an even number? Give the fraction in simplest form.

6.Compare the experimental probability of rolling a 3 with its theoretical probability. Which is larger, and by how much? Give both as fractions with denominator 60.

7.True or false? Because face 6 appeared 13 times, a fair die is more likely to roll a 6 than any other number on the next roll. Explain your choice.

8.The group rolls the die 600 more times. Explain what may happen to the experimental probability of rolling a 3 as the total number of rolls increases. Does it have to become exactly 1/6?

9.A student says, “The experimental probability is always the same as the theoretical probability.” Use the 60-roll results to give one piece of evidence that corrects this claim.