Fair Games, Odds, and Counting
Fair Game versus Fair Play
Fair Game—when everyone plays the game fairly by not cheating, playing by the rules, etc..
Fair Play—when each player of the game has an equal chance of winning the game.
The theoretical probability of each player winning a fair game is 1/2.
Tree Diagram—count success over total
P(Player 1) = 12/36 = 1/3
P(Player 2) = 24/36 = 2/3
P(Player 1) = 6/8 = 3/4
P(Player 2) = 2/8 = 1/4
Def: Odds—the ratio of the probability that an event will occur to the probability that the event will not occur.
Example: What are the odds of getting a “z” on this spinner?
= = 1/2 or 1:2
Experiment: Flip a coin twice
What are the odds of getting at least on head?
P(at least one head) = 3/4 Odds 3:1
Notice any patterns?
Odds of Player 2 winning are 2:1
Odds of Player 2 winning are 1:3
Odds are 5:1
Suppose you were to spin the two spinners below. Draw a tree diagram to find how many outcomes are possible.
Notice pattern: Why does this happen?
· First 2 characters are numbers
· Middle 3 characters are letters
· Last character is a number
How many license plates are possible?