In a clinical trial, a drug used to relieve pain caused side effects in 7% of the patients who took it. For a
new trial, two patients were selected at random. Find the probability that neither of the patients had side
effects
prob of side effect = .07
prob of no side effect = .93
prob(no side effect, no side effect) = (.93)^2 = .8649
How did you find the probability of no side effect ?
Either you have side effects or you don't have side effects
prob is a number between 0 and 1
so if prob(side effects) = .07
prob (no side effects) = 1 - .07 = .93
To find the probability that neither of the patients had side effects, we need to calculate the probability of each patient not having side effects and then multiply the individual probabilities together.
Let's assume that the probability of a patient having side effects is P(S) = 0.07, which means that the probability of a patient not having side effects is P(not S) = 1 - P(S) = 1 - 0.07 = 0.93.
Since the patients are selected at random, the probability that the first patient does not have side effects is 0.93. Similarly, the probability that the second patient does not have side effects is also 0.93.
To find the probability that both patients do not have side effects, we multiply the individual probabilities:
P(neither patient has side effects) = P(not S for patient 1) * P(not S for patient 2)
= 0.93 * 0.93
= 0.8649 or 86.49%
Therefore, the probability that neither of the patients had side effects is 0.8649 or 86.49%.