The probability that a certain hockey team will win any given game is 0.3786 based on their 13 year win history of 393 wins out of 1038 games played (as of a certain date). Their schedule for November contains 12 games. Let X = number of games won in November.
What is the expected number of wins for the month of November?
Well, let's do some math! The expected number of wins for the month of November can be calculated by multiplying the probability of winning a game (0.3786) with the total number of games to be played (12).
So, the expected number of wins for November is 0.3786 * 12 = 4.5432.
But hey, keep in mind that expected values are just predictions, and in sports, anything can happen! So, don't be too shocked if the team ends up with a different number of wins. Embrace the unpredictability and enjoy the game!
To find the expected number of wins for the month of November, we first need to calculate the probability of winning each game in November.
Given that the probability of winning any given game is 0.3786, the probability of losing a game would be 1 - 0.3786 = 0.6214.
Since the team has 12 games scheduled for November, we can use the binomial probability formula to find the probability of winning each number of games (k) out of 12. The formula is:
P(X = k) = (n choose k) * p^k * q^(n-k)
Where:
- n is the number of trials (12 games)
- k is the number of successes (wins)
- p is the probability of success (0.3786)
- q is the probability of failure (0.6214)
We can calculate the expected number of wins by multiplying the number of games (12) by the probability of winning each game (0.3786):
Expected number of wins = n * p
Expected number of wins = 12 * 0.3786 = 4.5432
Therefore, the expected number of wins for the month of November is approximately 4.5432.
To find the expected number of wins for the month of November, we can use the probability of winning any given game.
Given that the probability of winning a game is 0.3786, we can assume that this probability remains the same for each game in November.
Let's define the random variable X as the number of games won in November. X is a binomial random variable, as it represents the number of successes (wins) in a fixed number of independent trials (games) with the same probability of success (0.3786).
The expected value of a binomial random variable is given by the formula:
E(X) = n * p
where n represents the number of trials and p is the probability of success for each trial.
In this case, n is the number of games in November, which is 12, and p is the probability of winning a game, which is 0.3786.
Therefore, the expected number of wins in November can be calculated as:
E(X) = 12 * 0.3786
E(X) ≈ 4.5432
So, the expected number of wins for the month of November is approximately 4.5432.