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Common information for 3 and 4 The probability of contracting a stomach virus while visiting Mexico is 23%. Find the probability that amongst 12 students visiting Mexico 3. Exactly five students contract a stomach virus:

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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%.

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