Overall Notes

• There is one version of this assessment provided in the Teacher Resources Materials (TRM). Use this assessment as-is or use it as a model to create your own.

• If you are making your own assessment, consider using the test bank and the ExamView software.

 

Common Student Errors

• When making tree diagrams, students often have trouble with the values in the second set of branches. Remind students that these probabilities are conditional probabilities, where the condition is the outcome from the first stage of the diagram.

• Students sometimes make simple calculation errors when using a tree diagram. One strategy to avoid these errors is to ask students to calculate complete probabilities for all of the possibilities in the tree diagram, even if they are not needed to answer a question. This way, they can check that the sum of their probabilities is 1. If it isn’t, they will need to identify where they made a calculation mistake.

• Students will often incorrectly find the P(none) by calculating 1 – P(all). “none” and “all” are not complementary.

• Students often confuse permutations and combinations. Help them to remember that “order matters” for permutations and “order doesn’t matter” for combinations. A helpful tip is to explain to them that the combination lock for their locker is actually a permutation lock.

• Students will struggle with complex probability calculations that involve the multiplication counting principle and combinations. Try and help them to solve these problems in chunks, first thinking about the numerator and then thinking about the denominator. One option is to use quiz questions that scaffold students towards a final answer.