Discrete Mathematics Probability Revisions

I decided to make some changes in the order of presentation after teaching the probability lessons at the end of the counting unit. The particular lesson that I revised dealt with the discussion of discrete probability, uncovering probability rules, and working through examples.

What I found was that having students discuss what they knew about probability before working through the practice problems is that the class floundered because they lost site of the counting aspect of the problems and tried to make use of more familiar probability rules.

The three problems the class worked on were:

                                                                      i.      Probability dealt a black-jack

                                                                    ii.      Probability dealt a flush

                                                                  iii.      Probability dealt the queen of spades when four people playing hearts

I intend to have students use their counting techniques exclusively to find these probabilities before
diving into probability rules they may know. I can then connect their known rules back to these 
problems to show have they manifest themselves.

Here's the outline for having students go through probability rules:

     i.      Have students create list of rules they know
          1.      Rules to have
               a.      P(A or B) = P(A) + P(B) for mutually exclusive events
               b.      P(A and B) = P(A) x P(B) for independent events
               c.       0 <= P(A) <= 1
               d.      P(not A) = 1 – P(A)
               e.      sum of all probabilities = 1
               f.        may be others
          2.      Share out list and discuss
          3.      Students create examples of each rule using playing cards
               a.      Share and discuss

          4.      Cover additional rules not previously identified
          5.      Discuss connections between rules and the three problems previously worked on