Gambling and Probability

Grade 12 Lesson Plans (Based on 75-minute periods)

Lesson #2

N.B. Lesson #1 is planned for 45 minutes.

You may wish to start Lesson #2 at the end of Lesson #1 and add 30 minutes** to the in-class portion for Experiment #2.

Overall Description
This lesson requires students to learn about probability by conducting a variety of experiments. Students will also learn that chance is the essence of all gambling games and that probability describes the chance that something will happen but does not help anyone predict what actually will happen.
Curriculum Expectations
Overall Expectations
MBF3C - 2.0 Determine and represent probability, and identify and interpret its application (In MEL4E, not 3C))
MDM4U - 1.0 Solve problems involving the probability of an event or a combination of events for discrete sample places. (spaces?)
MDM4U - Solve problems involving the application of permutations and combinations to determine the probability of an event.
Teaching Strategies
Set the stage for doing probability experiments / Provide materials for doing probability experiments:
·  a roll of pennies
·  20 dice
·  decks of cards
Hand out the Black Line Master (BLM) 2.1, “Probability Experiments.”
Students work in pairs to complete the first two experiments / Facilitate and observe students working. Hand out the BLM 2.2, “Additional Probability Experiment.”
Whole-Group Discussion / Discuss the concept that inanimate objects do not have memories; therefore, the number of heads may or may not “even up.” Students should also notice that as the number of tosses increases, the percentages will tend to approach the expected values, but the difference between outcomes might decrease, stay the same, or even increase.
Brainstorm additional experiments / ·  Have students share ideas about carrying out similar experiments using either dice (including tetrahedral, octahedral, dodecahedral, or icosahedral dice) or playing cards. Have students answer questions such as, “Given that an outcome (e.g., the number 5 on a 6-sided die) has occurred X number of times more than any other number after 100 trials, will the number of occurrences of the other outcomes eventually catch up (with additional trials)?” This type of question is based on the assumption that each outcome (i.e., outcomes defined as a single face of a die or a specific card, suit, or denomination from a deck of cards) is equally likely.
·  Have students carry out several trials or even repeat the whole experiment several times. If computers are available, students may wish to use these experiments as simulations.
·  Hand out the Black Line Master 2.2, “Additional Probability Experiment.
Students work in pairs to complete the additional experiment. / Facilitate and observe students working. Assign the completion of the experiment for homework. Collect experiments at the beginning of the next class.
Timing
Set the stage for doing probability experiments. / 5 minutes
Students work in pairs to complete the first two experiments. / 15 minutes
Whole-Group Discussion / 5 minutes
Brainstorm additional experiments / 5 minutes
Students work in pairs to complete the additional experiment. / 45 minutes **+30 minutes
Assessment and Evaluation
Type / Description
Learning Skills Observations / Use checklist to observe the degree to which students remain on task and how well they work interdependently.
Formative / Collect the additional experiment for feedback regarding experimental design, data collection techniques, and analysis.
Resources
BLM 2.1 Probability Experiments
BLM 2.2 Additional Probability Experiment
Educator’s Guide, Section 2

Lesson 2

Grade 11 Foundations for College Mathematics

Grade 12 Mathematics of data Management, Mathematics for Work and Everyday Life

Probability Experiments

Coins, Dice, and Cards

Conduct the following experiments.

1. Flip a coin 20 times. Record your results in the table below.

a) How many heads are there?

b) How many tails are there?

c) Can you use this information to predict how many heads and tails will occur in the next 20 trials? Explain your thinking.

d) Flip the coin 20 more times. Record your results in the table below.

e) Is the number of heads and tails the same as your first result? Does this support or refute your answer to Part C? Explain your thinking.

2. Continue these two experiments (Part A and Part B) by tossing the coin an additiona1 50 times.

a)

Heads

/ 12 + ____
= ____

Tails

/ 2 + ____
= ____

Did the number of tails “catch up” to the number of heads? Yes No

What percentage of tosses is heads?

What percentage of tosses is tails?

Would you expect the number of tails to eventually catch up to the number of heads?

Why or why not?

b)

Heads

/ 212 + ____
= ____

Tails

/ 202 + ____
= ____

Did the number of tails catch up to the number of heads? Yes No

What percentage of tosses is heads?

What percentage of tosses is tails?

Would you expect the number of tails to catch up to the number of heads eventually?

Why or why not?

Compare your conclusions from the two experiments by referring to the actual number of heads and tails in each experiment and the percentage of heads and tails in each experiment.

Lesson 2, BLM 2.1

Grade 12 Math, MDM4U, MEL4E

Grade 11 Math MBF3C

Additional Probability Experiment

Lesson 2

Describe your experiment.

Collect your data in an organized manner.

What conclusions can you draw from your experiment? Explain fully.

Lesson 2, BLM 2.2

Grade 12 Math, MDM4U, MEL4E

Grade 11 Math MBF3C