Unit 4 S.CP.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.

Materials needed - lengths of rope, bags, red and white beans

First task (Developing Understanding): Human Venn Diagram
  • Make a "human Venn diagram" where the sample space is all the students in the class. Use lengths of rope to create three overlapping circles. Assign an event to each of the three circles, such as: has a dog, has a job, and went to bed before 11:00 P.M. Have students place themselves in the appropriate locations.
  1. What is the probability that a student chosen at random has a dog, given that they went to bed before 11:00 P.M.?
  2. What is the probability that a student chosen at random went to bed before 11:00 P.M., given that they have a job?
  3. What is the probability that a student chosen at random has a dog, given that they have a job and went to bed before 11:00 P.M.?

Second task (Solidify Understanding): Two-way Table
  • Give them data in a Venn diagram from the Vitamin C/Placebo, Cold/No Cold (see USOE Curriculum Guides II.4.S.CP.6). Create a two-way frequency table. Use the data to support or disprove that taking Vitamin C is effective in preventing a cold.

Third task (Practice Understanding): Beans in a Bag
  • Give each group a bag of dry red and white beans.
  • Rules - you may only remove two beans at a time (one bean, then another), then you must replace the beans.
  • Gather data for a few minutes.
  • Organize your data in a two-way table, Venn diagram, and tree diagram.
  • Estimate each probability:
    • P(second bean is red | first bean is white)
    • P(second bean is red | first been is red)
    • P(second bean is red (intersection symbol) first bean is white)
    • P(a bean is red)
  • If there are 34 red beans, how many white beans are there?