The World Series ends when a team wins 4 games. Suppose that sports analysts con

Question

The World Series ends when a team wins 4 games. Suppose that sports analysts consider one team to be stronger and give them a 60% chance of winning any individual game. a) Explain how you would use randomly generated numbers from 0 to 9 to model the likelihood that the underdog team will win. b) Run 20 trials and create a table of your findings. For your table, use the headings “Trial Number”, “Components”, “Outcome”. c) Answer the question: What is the likelihood that the underdog will win the World Series.

Explanation / Answer

c)

probability of winning strong team = 0.60

probability of winning underdog = 1-0.60 = 0.4

Here is my explanation:
The underdog winning the world series can be a result of four scenarios
a) 4 W - 0 L (a four game series)
b) 4 W - 1 L (a five games series)
c) 4 W - 2 L (a six game series)
d) 4 W - 3 L (a seven game series)

The probability of these occuring are:
a) .40*.40*.40*.40*1(because a four game sweep only happens 1 way-first four games) = 0.0256

b) .40*.40*.40*.40*.60*4 (because the favorite could have won any one of the first 4 games) = 0.06144

c) .40*.40*.40*.40*.60*.60*10 (because the favorite could have won two games in 10 different combinations) = 0.09216

d) .40*.40*.40*.40*.60*.60*.60*20 (because the favorite could have won three games in 20 different combinations) = 0.110592

We CANNOT use 7C4 because the favorite cannot win game 7. If the underdog wins all 4 games by game 6 there is no game 7!

*Note how with each additional game won by the favorite, the probability goes up

Since any of these outcomes a-d result in the underdog winning the world series we add up all the probabilities and get:

28.97 % chance the underdog wins the world series

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