Preparing for the next class
In the next in-class activity, you will need to construct a probability model to describe simple chance experiments, calculate the probability of a particular event using probabilities given in a table, and begin to think critically about the number of “successes” that would occur if a chance experiment were repeated multiple times.
A probability model includes all possible outcomes of a chance experiment and the probabilities associated with those outcomes.
Imagine a fair spinner with 3 equally-sized sections: 1 section is red, 1 section is blue, and 1 section is yellow. If we spin the spinner, all 3 outcomes are equally likely, so the probability of each outcome is one-third. The following table displays the probability model.
| Outcome | Probability |
| Red | 1
3 |
| Yellow | 1
3 |
| Blue | 1
3 |
Let’s consider another chance experiment: rolling a fair, 6-sided die.
Question 1
Fill in the following table to create a probability model for the outcomes that may occur when you roll a fair, 6-sided die. Represent the probabilities using fractions.
| Outcome | Probability |
Hint: Dice have 6 sides that are labeled with the numbers 1–6, and since the die is fair, each of these outcomes is equally likely.
Question 2
If you roll a fair die, what is the probability that the die will land on a number that is less than or equal to 2? Write your answer as a simplified fraction.
Hint: Use the probability rules you learned in In-Class Activity 7.B. We can rephrase the question by asking, “What is the probability that the die will land on 1 or 2?”
Question 3
If you roll a fair die, what is the probability that the die will land on a number that is in the range [1, 6]? Note that the endpoints, 1 and 6, are included in the range.
Hint: This range includes all possible outcomes of rolling a 6-sided die. Now let’s consider another chance experiment: flipping a fair coin.
Question 4
Fill in the following table to create a probability model for the outcomes that may occur when you flip a fair coin. Represent the probabilities using decimals.
| Outcome | Probability |
Hint: There are two possible ways that a coin can land. Since the coin is “fair,” these two outcomes are equally likely.
Question 5
If you flip a coin 10 times, are you guaranteed to get exactly 5 heads?
Hint: Remember the Law of Large Numbers that you learned about in In-Class Activity 7.A.
Looking ahead
Sometimes we carry out a chance experiment multiple times and count the number of “successes.” To describe this scenario, we could use a probability distribution, which lists all possible values of a random variable and the probabilities associated with those values.
Question 6
Suppose we flip a coin twice. Complete the list of possible values below.
- Tails on the first flip and heads on the second flip
- Heads on the first flip and tails on the second flip
Hint: The list should include all possible combinations of heads and tails for the two flips.
Question 7
Fill in the following table to complete the probability distribution for the number of heads that would occur in 2 coin flips.
| Number of Heads | Probability |
| 0 | #
$ = 0.25 |
| 1 | |
| 2 |
Hint: There are 4 possible outcomes for a set of 2 coin flips, and only one of them results in 0 heads. That is why the probability of getting 0 heads is one-fourth.
