options: Summarize and describe distributions.

Develop understanding of statistical variability.

Draw informal comparative inferences about two populations.

Understand and evaluate random processes underlying statistical experiments.

Calculate expected values and use them to solve problems.

Use random sampling to draw inferences about a population.

Interpret linear models.

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

Investigate patterns of association in bivariate data.

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

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

Use probability to evaluate outcomes of decisions.

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

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

Understand independence and conditional probability and use them to interpret data.
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: 14