options: Calculate expected values and use them to solve problems.

Draw informal comparative inferences about two populations.

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

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

Investigate patterns of association in bivariate data.

Summarize and describe distributions.

Use probability to evaluate outcomes of decisions.

Use random sampling to draw inferences about a population.

Understand and evaluate random processes underlying statistical experiments.

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

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

Interpret linear models.

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

Develop understanding of statistical variability.

Summarize, represent, and interpret data on a single count or measurement variable.
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: 10