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=Welcome to Probability and Baseball!= Created By: Cathy Dignazio

This site was created to show students how to make predictions using probability...while having fun with baseball statistics.

How to Use this Site
Students will predict the number of games played for an MLB championship series win.

Directions for Students
Students should work in pairs for this activity.

__Materials Needed__: calculator, sports page of newspaper or access to other published baseball statistics

1. Given the number of games in a championship series, find the total number of possible outcomes. In a 7 game series, one possible combination of outcomes is EWWEEWW, where E is the East Division and W is West Division. Remember to consider that not all 7 games must be played to win the series! A 7 game series can be won in 4, 5, or 6 games as well. All combinations for winning the series must be considered. List all possible outcomes.
 * //Remember//** that the winning team always wins the last game.

2. Create a table showing the number of possible outcomes for the series (Hint: number of sequences for number of games played for 4, 5, 6, and 7 game series).

3. Create a table of odds favoring your team for 1:1, 2:1, 3:1 odds for a 4, 5, 6, and 7 game series. __Recall:__ if odds are m:n, then p = m/(m +n). __Recall__: p + q = 1. For example, if the odds are 1:1 then p = 1(1 +1) = 1/2 and q = 1 - p = 1/2 For a 5 game series, we will need to recall that there are 8 possible game sequences for a 5 game series. The probability that E will win is P(E in 5) : qpppp + pqppp + ppqpp + pppqp = 4p 4 q AND the probability that W will win is P(W in 5) = pqqqq + qpqqq + qqpqq + qqqpq = 4pq 4 The total probability of a 5 game series is the sum of all probabilities which is P(5 game series) = P(E in 5) + P(W in 5) = 4p 4 q + 4pq 4 = 4(1/2) 4 (1/2) + 4(1/2)(1/2) 4 = 0.25

Our table should look like this:

4. Based on the odds in favor of your team, predict the number of games that will be played to win the series. Recall that E(X) = sum of X i P(X i ). For example for 1:1 odds E(X) = 4[P(4 game series)] + 5[P(5 game series)] + 6[P(6 game series)] + 7[P (7 game series)]
 * odds in favor of E || 1:1 || 2:1 || 3:1 ||
 * P( 4 game series) ||  ||   ||   ||
 * P (5 game series) || .25 ||  ||   ||
 * P (6 game series) ||  ||   ||   ||
 * P (7 game series) ||  ||   ||   ||
 * E (X) ||  ||   ||   ||

5. Complete the table with all E(X) calculations for 1:1, 2:1, and 3:1 odds in favor of your team.

6. What are these results telling you about your team? About the series?

7. Look up published odds for the series. Can you predict the number of games that will be played for your team to win the series?

8. Share your predictions and tabulated results with the class. Compare your results with other teams in the class.

Grading Rubric Grading Rubric

Information for Educators Enduring Understandings, Essential Questions, and NCTM Standards