describe the likelihood that events will happen, and use that information to make predictions
solve various problems that involve probability, using appropriate tools and strategies, including Venn and tree diagrams
Give students data that they can display in a Venn diagram and then use to determine the probability of an event. For example, in a class of 30 students, 19 students like mystery novels, 17 students like adventure novels, and 15 students like both types of novels. What is the probability of students liking neither adventure nor mystery novels?
determine and compare the theoretical and experimental probabilities of multiple independent events happening and of multiple dependent events happening
To determine the theoretical probabilities of an event, have students first create a tree diagram or make an organized list to determine all possible outcomes and then identify the outcomes that are of interest.
For example, below are all possible outcomes for tossing one coin, three times, where the outcomes of interest are tossing two tails and one head: HTT, THT, and TTH. The theoretical probability for tossing two tails and one head is .
Have students design two probability simulations in which two to five numbers from 1 to 15 are randomly generated for 10, 30, and 100 trials. One of the simulations should allow for numbers to be repeated (independent events). The other simulation should not allow for numbers to be repeated (dependent event).
Have students determine the experimental probabilities of only odd numbers being generated by each of the simulations and compare these to the theoretical probabilities for each simulation.