Based on the 2017 season, the Houston Astros have a
winning percentage of .623. Use the binomial model to
find the probability that the Astros will win 4 of their next 6
games.
P (x) = [ ]
n!
x!(n−x)!
p
xq
n−x
12.4%
24.7%
32.1%
62.3%
In the binomial model, we use the formula:
P(x) = nC x * p^x * (1-p)^(n-x)
where n is the number of trials, x is the number of successes, p is the probability of success in a single trial, and (1-p) is the probability of failure in a single trial.
In this case, the Astros have a winning percentage of 0.623, so the probability of success in a single game is 0.623. The number of trials is 6 (the number of games they will play), and we want to find the probability of winning 4 out of the 6 games.
Using the formula, we have:
P(4) = 6C4 * 0.623^4 * (1-0.623)^(6-4)
= 15 * 0.623^4 * 0.377^2
≈ 0.321
Therefore, the probability that the Astros will win 4 of their next 6 games is approximately 32.1%.