In a clinical trial, a drug used to relieve pain caused side effects in 9% of the patients who took it. For a new trial, three patients were selected at random. Find the probability that none of those patients had side effects.
prob side effect = 9/100
prob of no side effects = 91/100
prob that of three none has side effects
= (91/100)^3 = .753571
To find the probability that none of the three patients had side effects, we need to calculate the probability for each patient and then multiply them together.
Given that the drug caused side effects in 9% of the patients, we can say that the probability of a patient having side effects is 0.09. Therefore, the probability of a patient not having side effects is 1 - 0.09 = 0.91.
Since we have three patients and we want to find the probability that none of them had side effects, we need to multiply the individual probabilities together.
P(none of the patients has side effects) = P(patient 1 has no side effects) * P(patient 2 has no side effects) * P(patient 3 has no side effects)
P(none of the patients has side effects) = 0.91 * 0.91 * 0.91
Calculating this product would give you the final probability that none of the three patients had side effects.