Probability Strategies Review
Remember at the beginning of the chapter when we expressed our disdain for probability formulas? This activity will bring that idea full circle. Notice where formulas stand in our list of possible strategies to use for solving probability questions:
- Sample Space
- Venn Diagram
- Two-way Tables
- Tree Diagrams
- Formulas (last resort)
Have students list an example problem for each strategy. Ideally this is the example problem that you used in class to introduce the strategy. This context will help them to remember what the strategy looks like.
“OR” versus “AND”
So let’s say you have to resort to using a formula. How do you know which one to use? First, you must decide whether the problem is an “OR” or and “AND” problem. Then follow the flowchart to arrive at the right formula.
Mutually Exclusive versus Independent
Ask students to define mutually exclusive or to define independent and they will probably give you the same answer for each:
“One doesn’t affect the other!”
Well…sort of. But we need to get much more technical here.
Two events A and B are mutually exclusive if they have no outcomes in common and so can never occur together.
Two events A and B are independent events if knowing whether or not one event has occurred does not change the probability that the other event will happen.
The question of whether two events are mutually exclusive is a totally different question from asking if they are independent. This Activity forces students to come up with their own examples of events that fit certain criteria. Essentially it forces them to think about the definition of mutually exclusive and the definition of independent in many different contexts. Pro teacher tip: #3 is impossible unless one of the events has a probability of zero (i.e. roll a die. A –> getting a 9. B –> getting a 4). Your overachievers might be interested in a proof for this one.