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Mathematics > Course Model Mathematics II (Integrated Pathway) > Conditional Probability and the Rules of Probability
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Mathematics | Course : Model Mathematics II (Integrated Pathway)

Domain - Conditional Probability and the Rules of Probability

Cluster - Understand independence and conditional probability and use them to interpret data from simulations or experiments.

[MII.S-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.* For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.

Resources:


  • Independently combined probability models
    Two probability models are said to be combined independently if the probability of each ordered pair in the combined model equals the product of the original probabilities of the two individual outcomes in the ordered pair.
  • Probability
    A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, testing for a medical condition).
  • Sample space
    In a probability model for a random process, a list of the individual outcomes that are to be considered.

Predecessor Standards:

  • 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. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • MII.S-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.*
  • MII.S-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.*
  • MII.S-CP.A.5
    Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.* For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.
  • MII.S-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.*