Answer:
10%
Explanation:
The probability of no patients having undesirable side effects is calculated using the binomial distribution formula. The formula is:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
where:
P(X = k) is the probability of getting k successes in n trials
C(n, k) is the number of combinations of n things taken k at a time
p is the probability of success on any given trial
(1 - p) is the probability of failure on any given trial
In this case, we have:
n = 8 (since there are 8 patients in the sample)
p = 0.25 (since 25% of all patients who use the drug have undesirable side effects)
k = 0 (since we want to find the probability that none have undesirable side effects)
Plugging these values into the formula, we get:
P(X = 0) = C(8, 0) * 0.25^0 * (1 - 0.25)^(8 - 0) = 1 * 1 * 0.10011291504 ≈ 0.100
Therefore, the probability that none of the eight patients in the sample have undesirable side effects is approximately 0.100 or 10%