In testing a new drug, researchers found that 10% of all patients using it will have a mild side effect. A random sample of 12 patients using the drug is selected. If you wanted to find the probability that exactly three will have this mild side effect, what would be the values of n, x, and p that you would use to look this probability up in the Binomial Probability table (A-1), AND what would be the probability

To find the probability that exactly three patients out of a random sample of 12 will have this mild side effect while using the drug, we can use the binomial distribution.

In the binomial distribution, we have three main components: n, x, and p.

1. n represents the number of trials, which is the number of patients in the sample. In this case, n is equal to 12, as we have a random sample of 12 patients.

2. x represents the number of successful outcomes, which is the number of patients who will have the mild side effect. In this case, x is equal to 3 since we want to find the probability of exactly three patients having this side effect.

3. p represents the probability of success in a single trial, which is the probability of a patient having the mild side effect. In this case, p is equal to 0.10, as we are given that 10% of all patients using the drug will have this mild side effect.

Using these values, we can look up the probability in the binomial probability table.

To find the probability, we can use the binomial probability formula:

P(X = x) = (nCx) * p^x * (1-p)^(n-x)

where (nCx) represents the binomial coefficient, which can be calculated as:

(nCx) = n! / [x! * (n-x)!]

With n = 12, x = 3, and p = 0.10, we can substitute these values into the formulas and calculate the probability:

P(X = 3) = (12C3) * 0.10^3 * (1-0.10)^(12-3)

Calculating (12C3) = 12! / (3! * (12-3)!) = 220

P(X = 3) = 220 * 0.10^3 * 0.90^(12-3)

P(X = 3) ≈ 0.228

So, the probability of exactly three out of 12 patients having this mild side effect is approximately 0.228.