few_shots: Example:
Problem/activity:
You’re mixing ingredients for cookies. The recipe says to combine 6 tablespoons, or ¾ stick, of butter with 1 cup of sugar. You accidentally mix in a whole stick of butter (8 tablespoons) with the cup of sugar. How can you fix this?


Mathematical concept/skill options: 
A. Analyze proportional relationships and use them to solve real-world and mathematical problems.
B. Understand ratio concepts and use ratio reasoning to solve problems.


Your response:
{
  "explanation": "This problem focuses on the ratio between two ingredients. Students do not have to analyze proportional relationships in-depth, which is reserved for a higher grade level, but rather use ratios to find missing values.",
  "answer": "B"
}

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_000972

6
options: Understand independence and conditional probability and use them to interpret data.

Develop understanding of statistical variability.

Understand and evaluate random processes underlying statistical experiments.

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

Investigate patterns of association in bivariate data.

Interpret linear models.

Use random sampling to draw inferences about a population.

Draw informal comparative inferences about two populations.

Use probability to evaluate outcomes of decisions.

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

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

Summarize and describe distributions.

Calculate expected values and use them to solve problems.

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

Summarize, represent, and interpret data on two categorical and quantitative variables.
problem_activity: Problem 1
You are in a diner and want to know if choosing cream or sugar are independent events, that is, if one depends on the other. Below is a Venn diagram that represents the number of people in the diner one morning. A random person is chosen.
[IMG]
Is this random person more likely to have cream in his coffee if he has sugar? Calculate the probability.
Is this random person more likely to have sugar in his coffee if he has cream? Calculate the probability
Problem 2
A coin is tossed and a single six-sided die is rolled. If landing on heads is represented by
$$H$$
and rolling a
$$3$$
is represented by
$$R$$
, determine if the following is true:
$$P(H \space and \space 3)=P(H)\cdot P(3)$$


correct_option_index: 0