Question

he probability that the San Jose Sharks will win any given game is 0.3694 based on a 13-year win history of 382 wins out of 1034 games played (as of a certain date). An upcoming monthly schedule contains 12 games. What is the probability that the San Jose Sharks win 9 games in that upcoming month

Answer 1

Answer:

0.0071 = 0.71% probability that the San Jose Sharks win 9 games in the upcoming month.

Step-by-step explanation:

For each game, there are only two possible outcomes. Either the Sharks win, or they do not. The probability of the Sharks winning a game is independent of any other game. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The probability that the San Jose Sharks will win any given game is 0.3694.

This means that $p = 0.3694$

An upcoming monthly schedule contains 12 games.

This means that $n = 12$

What is the probability that the San Jose Sharks win 9 games in the upcoming month?

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 9) = C_{12,9}.(0.3694)^{9}.(0.6306)^{3} = 0.0071$

0.0071 = 0.71% probability that the San Jose Sharks win 9 games in the upcoming month.