Question

it is known that a certain drug causes side effects in 10 % of patients. if we consider a random sampling of 12 patients, what is the probability less it is known that a certain drug causes side effects in 10 % of patients. if we consider a random sampling of 12 patients, what is the probability less than two have the side effect?than two have the side effect?

Answer 1

The probability of less than two patients having the side effect can be calculated using the binomial distribution. We can use the formula:

P(X < 2) = P(X = 0) + P(X = 1)

where X is the number of patients who have the side effect, and P(X = k) is the probability of k patients having the side effect.

The probability of a patient having the side effect is 0.10, so the probability of a patient not having the side effect is 0.90.

Using the binomial distribution formula, we can calculate:

P(X = 0) = (0.90)^12 = 0.2824
P(X = 1) = 12(0.10)(0.90)^11 = 0.3766

Therefore:

P(X < 2) = P(X = 0) + P(X = 1) = 0.2824 + 0.3766 = 0.6590

So the probability of less than two patients having the side effect is 0.6590, or about 66%.