Exercise 1: Theoretical Probability

In this exercise, you are going to use the knowledge you have learned to determine the theoretical probability of flipping a single coin and rolling a pair of dice.

1. First, create a tree diagram to count the possible outcomes of this probability experiment.

2. Write the sample space for this experiment. You may use a simple code format, such as H15 represents heads on the coin flip, a 1 on the first die and a 5 on the second die. How many total outcomes are possible?

3. Use the Fundamental Counting Principle to show that your answer to Number 2 is correct.

4. What is the probability that you will get tails on the coin flip and roll two odd numbers on the dice?

5. What is the probability that the sum of the two dice will be greater than 8?

6. What is the probability that you flip heads on the coin and the sum of the two dice is an even number?

7. How many different outcomes are possible if you know that the coin flip landed on tails?

8. What is the probability that the coin flip lands on heads, the first number on the die is less than 4, and the second number is greater than 2?

Exercise 2: Empirical (Experimental) Probability

In this exercise, you are going to complete the probability experiment from the previous exercise and record your results. Complete the processes in order: flip a coin, record the result, roll one die, record the result, roll the second die (or the first one a second time if you only have one), record the result. Then repeat the process.

1. To get a sense of what is happening, you will need to do this multiple times, so do enough trials to fill the table below.

Trial #	Coin Flip	Roll 1	Roll 2
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29

2. Record all of your outcomes below along with their frequency (How many times did each outcome happen?). This is your sample of experimental data.

3. Determine the experimental probability of all of your outcomes. Remember that the experimental probability is the frequency (or count) divided by the total number of trials!

4. Compare your theoretical probabilities to the experimental ones. Are they similar? Did any of your outcomes or probabilities match the probabilities from Exercise 1? What similarities or differences did you see? You should provide specific details from your data when you answer this question..