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, in json format:
{
  "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: Develop understanding of statistical variability.

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

Interpret linear models.

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.

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

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

Use random sampling to draw inferences about a population.

Use probability to evaluate outcomes of decisions.

Draw informal comparative inferences about two populations.

Calculate expected values and use them to solve problems.

Investigate patterns of association in bivariate data.

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

Summarize and describe distributions.
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: 5