options: Summarize, represent, and interpret data on two categorical and quantitative variables.

Understand and evaluate random processes underlying statistical experiments.

Understand independence and conditional probability and use them to interpret data.

Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

Use probability to evaluate outcomes of decisions.

Draw informal comparative inferences about two populations.

Interpret linear models.

Calculate expected values and use them to solve problems.

Investigate chance processes and develop, use, and evaluate probability models.

Summarize and describe distributions.

Investigate patterns of association in bivariate data.

Develop understanding of statistical variability.

Summarize, represent, and interpret data on a single count or measurement variable.

Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Use random sampling to draw inferences about a population.
problem_activity: Problem 1
Each scenario on the left corresponds with a calculation on the right. Connect the scenarios and calculations and identify which features are most useful in connecting the representations:
|              Rolling once the number is an odd number or a number less than 3.              | $${P(A\space\mathrm{and}\space B) = \left({3\over6}\right)\left({1\over6}\right)}$$ |
|---------------------------------------------------------------------------------------------|-------------------------------------------------------------------------------------|
|                     Rolling once and the number is an odd number or 4.                      |         $${P(A\space\mathrm{or}\space B) = {3\over6}+{2\over6}-{1\over6}}$$         |
| Rolling twice. The first roll is an odd number and the second roll is a number less than 3. | $${P(A\space\mathrm{and}\space B) = \left({3\over6}\right)\left({2\over6}\right)}$$ |
|         Rolling twice. The first roll is an odd number and the second roll is a 4.          |              $${P(A\space\mathrm{or}\space B) = {3\over6}+{1\over6}}$$              |
Problem 2
Below is a spinner with four quadrants, each labeled 1–4. Each outcome is equally likely.
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Sam spins the spinner twice and doesn’t land on 4. What is the probability of this occurring?
Problem 3
Allison has put together a simple game. She put 6 cubes in a paper bag—3 yellow and 3 blue. Allison has determined that the rules are as follows:
Pull a cube from the bag and put it on the table.
Pull a second cube from the bag.
If the cubes are different colors, then Player A wins.
If the cubes are the same color, then Player B wins.
Is this game fair? How do you know?


correct_option_index: 2