Question

A school has 500 students. Usually, there are an average of 20 students who are absent. If a sample of 30 students is taken on a certain day, what is the probability that at least 2 students in the sample will be absent?

a) 0.0228

b) 0.9772

c) 0.9772

d) 0.0228

Answer 1

To find the probability of at least 2 students being absent from a sample of 30, calculate the probabilities of each possible outcome and add them up.

Step-by-step explanation:

To find the probability that at least 2 students in the sample will be absent, we need to calculate the probabilities of exactly 2, exactly 3, and so on, up to exactly 30 students being absent and then add them up.

To calculate each probability, we can use the formula for the probability of exactly k successes in n trials, given by:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where C(n, k) represents the number of combinations of n items taken k at a time, p is the probability of success (in this case, the probability of a student being absent), and n is the number of trials (in this case, the size of the sample).

Once we have calculated the probabilities for each outcome, we can add them together to find the probability of at least 2 students being absent in the sample.