Final answer:
To find the probability that a patient felt relief and were administered the drug, multiply the probabilities of the two events. The probability of event F occurring on the second trial can be found by considering the probabilities of both trials separately.
Step-by-step explanation:
a. To find the probability that a randomly selected patient felt relief and were administered the drug, we need to find the intersection of the events 'felt relief' and 'administered the drug'. This can be done by multiplying the probabilities of these two events. Let's say the probability of feeling relief is p and the probability of being administered the drug is q. Then the probability of both events happening is p * q.
b. To find the probability that 'event F' (rolling a four or five) occurs for the first time on the second trial, we need to consider the probability of not rolling a four or five on the first trial and then rolling a four or five on the second trial. The probability of not rolling a four or five on the first trial is 4/6 or 2/3. The probability of rolling a four or five on the second trial is 2/6 or 1/3. To find the probability of both events happening, we multiply these probabilities: (2/3) * (1/3).