Answer:
The probability that exactly five students out of 12 contract a stomach virus while visiting Mexico is approximately 0.2707 or 27.07%.
Explanation:
To find the probability that exactly five students out of 12 contract a stomach virus while visiting Mexico, we can use the binomial probability formula.
The formula is P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
where X is the number of students who contract the virus, k is the specific number we're interested in (in this case, 5), n is the total number of students (12), p is the probability of one student contracting the virus (0.23), and "n choose k" is the binomial coefficient - the number of ways to choose k objects out of n, which can be calculated using the formula n!/(k!(n-k)!).
Using these values, we get:
P(X=5) = (12 choose 5) * 0.23^5 * (1-0.23)^(12-5)
= 792 * 0.0009765625 * 0.3457171406
= 0.2706918748
Therefore, the probability that exactly five students out of 12 contract a stomach virus while visiting Mexico is approximately 0.2707 or 27.07%.