In a clinical trial, a drug used to reduce blood pressure caused side effects in 6% of the patients who took it. For a new rial, two patients were selected at random. Find the probability that both the patients had side effects.
To find the probability that both patients had side effects, we can calculate the probability of one patient having side effects and multiply it by the probability of the second patient also having side effects.
Given that the drug caused side effects in 6% of the patients who took it, we can assume that the probability of a patient having side effects is 0.06.
So, P(Side Effects for Patient 1) = 0.06
Since the patients were selected at random, the probability of the second patient also having side effects is the same as the first patient, i.e., P(Side Effects for Patient 2) = 0.06.
Now, we can calculate the probability that both patients had side effects by multiplying the individual probabilities:
P(Both Patients with Side Effects) = P(Side Effects for Patient 1) * P(Side Effects for Patient 2)
= 0.06 * 0.06
= 0.0036
Therefore, the probability that both patients had side effects is 0.0036, or 0.36%.