Question

1)

a) Last year, the Toronto Maple Leafs won 46 games. Calculate the probability that, over an 82 game season, an average strength team (p=0.5) wins 46 games or more.  

b) Calculate the probability for an average team (p=0.5) to win 9 games in a row.

c) Last year, the team lost 21 out of 26 games. Calculate the probability for an average team (p=0.5) to win 5 games or less out of 26 games.

Please include all the necessary equations as I need to code this.

Answer 1

a) Last year, the Toronto Maple Leafs won 46 games. Calculate the probability that, over an 82 game season, an average strength team (p=0.5) wins 46 games or more.

Let X = total number of win

p = probability of winning of the average team = 0.5

n = total number of games = 82

Here we want to find P(X >= 46) = 1 - P(X <= 45) ......( 1 )

Let's use binomial distribution in excel:

P(X <= 45) = "=BINOMDIST(45,82,0.5,1)" = 0.8399

P(X >= 46) = 1 - 0.8399 = 0.1601

b) Calculate the probability for an average team (p=0.5) to win 9 games in a row.

p^n = 0.5⁹ = 0.001953

c) Last year, the team lost 21 out of 26 games. Calculate the probability for an average team (p=0.5) to win 5 games or less out of 26 games.

Here n = 26, p = 0.5

and we want to find p( X <= 5) = "=BINOMDIST(5,26,0.5,1)" = 0.0012