[b][size=200][i]MA.912.DP.4 Use and interpret independence and probability[/i][/size][br][br][/b][size=150][b]MA.912.DP.4.1:[/b] Describe events as subsets of a sample space using characteristics, or[br]categories, of the outcomes, or as unions, intersections or complements of other event[br][br][b]MA.912.DP.4.2:[/b] Determine if events A and B are independent by calculating the product of[br]their probabilities. [br][br][b]MA.912.DP. 4.3[/b]: Calculate the conditional probability of two events and interpret the result in[br]terms of its context.[br][br][b]MA.912.DP.4.4:[/b] Interpret the independence of two events using conditional probability. [br][br][b]MA.912.DP.4.5[/b]: Given a two-way table containing data from a population, interpret the joint[br]and marginal relative frequencies as empirical probabilities and the conditional relative frequencies as empirical conditional probabilities. Use those probabilities to determine whether characteristics in the population are approximately independent. [br][br][b]MA.912.DP.4.6:[/b] Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.[br][br][b]MA.912.DP.4.7: [/b]Apply the addition rule for probability, taking into consideration whether the[br]events are mutually exclusive, and interpret the result in terms of the model and its context.[br][br][b]MA.912.DP.4.8: [/b]Apply the general multiplication rule for probability, taking into consideration whether the events are independent, and interpret the result in terms of the context[br][br][b]MA.912.DP.4.9:[/b] Apply the addition and multiplication rules for counting to solve mathematical and real-world problems, including problems involving probability[br][b]MA.912.DP.4.10:[/b] Given a mathematical or real-world situation, calculate the appropriate[br]permutation or combination[br][/size][br][b] [size=200][i]MA.912.DP.6 Use probability distributions to solve problems. [/i][/size][br][br][/b][size=150][b]MA.912.DP.6.1:[/b] Define a random variable for a quantity of interest by assigning a numerical[br]value to each individual outcome in a sample space; graph the corresponding[br]probability distribution using the same graphical displays as for data[br]distributions.[br][br][b]MA.912.DP.6.2:[/b] Develop a probability distribution for a discrete random variable using[br]theoretical probabilities. Find the expected value and interpret it as the mean[br]of the discrete distribution.[br][br][b]MA.912.DP.6.3[/b]: Develop a probability distribution for a discrete random variable using[br]empirical probabilities. Find the expected value and interpret it as the mean[br]of the discrete distribution.[br][br][b]MA.912.DP.6.4:[/b] Given a binomial distribution, calculate and interpret the expected value. Solve real-world problems involving binomial distributions.[br][br][b]MA.912.DP.6.5[/b] Solve real-world problems involving geometric distributions. [/size]