Probability

Standards

• CCSS.MATH.CONTENT.7.SP.C.5 — Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
• CCSS.MATH.CONTENT.HSS.CP.B.8 — (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.
• CCSS.MATH.CONTENT.HSS.CP.A.2 — Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
• CCSS.MATH.CONTENT.HSS.MD.A.2 — (+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
• CCSS.MATH.CONTENT.HSS.MD.A.4 — (+) Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.
• CCSS.MATH.CONTENT.7.SP.C.7.A — Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.
• CCSS.MATH.CONTENT.7.SP.C.8.A — Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
• CCSS.MATH.CONTENT.HSS.CP.A.4 — Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.
• CCSS.MATH.CONTENT.HSS.CP.B.7 — Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.
• CCSS.MATH.CONTENT.HSS.CP.B.6 — Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model.
• CCSS.MATH.CONTENT.8.SP.A.4 — Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.
• CCSS.MATH.CONTENT.HSS.MD.A.3 — (+) Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.
• CCSS.MATH.CONTENT.7.SP.C.6 — Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.
• CCSS.MATH.CONTENT.HSS.CP.B.9 — (+) Use permutations and combinations to compute probabilities of compound events and solve problems.
• CCSS.MATH.CONTENT.HSS.MD.A.1 — (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.
• CCSS.MATH.CONTENT.HSS.MD.B.5.A — Find the expected payoff for a game of chance.
• CCSS.MATH.CONTENT.HSS.CP.A.3 — Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
• CCSS.MATH.CONTENT.HSS.CP.A.1 — Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not").
• CCSS.MATH.CONTENT.HSS.MD.B.7 — (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game)
• CCSS.MATH.CONTENT.7.SP.C.8 — Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
• CCSS.MATH.CONTENT.7.SP.C.7.B — Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.
• CCSS.MATH.CONTENT.HSS.CP.A.5 — Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
• CCSS.MATH.CONTENT.HSS.MD.B.5.B — Evaluate and compare strategies on the basis of expected values.
• CCSS.MATH.CONTENT.HSS.MD.B.6 — (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
• CCSS.MATH.CONTENT.HSS.MD.B.5 — (+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.