Final answer:
The probability that the school's football team will win exactly 2 out of their next 5 games, according to Han's information, is approximately 0.2138.
Step-by-step explanation:
To find the probability that the school's football team will win exactly 2 out of their next 5 games, we need to use the binomial probability formula. The formula is:
P(X = k) = C(n, k) * p^k * q^(n-k)
Where P(X = k) is the probability of exactly k successes, n is the number of trials, p is the probability of success, and q is the probability of failure. In this case, n is 5 (the number of games), k is 2 (the number of desired successes), p is the probability of winning a game (0.3694), and q is the probability of losing a game (1 - 0.3694 = 0.6306).
Plugging the values into the formula, we get:
P(X = 2) = C(5, 2) * (0.3694)^2 * (0.6306)^(5-2)
Simplifying the formula, we get:
P(X = 2) = 10 * (0.3694)^2 * (0.6306)^3
Calculating the expression, we get:
P(X = 2) ≈ 0.2138
Therefore, the probability that the school's football team will win exactly 2 out of their next 5 games, according to Han's information, is approximately 0.2138.