Doctors conducting a pharmaceutical study release the following information: The probability that a patient will receive a trial medication in the first round is 11/40;

 Doctors conducting a pharmaceutical study release the following information:

The probability that a patient will receive a trial medication in the first round is 11/40;
The probability that a patient will receive a placebo medication in the second round given that they received a trial medication in the first round is 1/3;
The probability that a patient will receive a placebo medication in the second round is 7/10.
Let event A be the event that a patient receives a trial medication in the first round and event B be the event that a patient receives a placebo medication in the second round. Are events A and B mutually exclusive, independent, both, or neither?

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Events A and B are mutually exclusive.

Events A and B are independent.

Events A and B are neither mutually exclusive nor independent.

Events A and B are both independent and mutually exclusive.

Answer Explanation
Correct answer:
Events A and B are neither mutually exclusive nor independent.

The correct conclusion is that the events are neither mutually exclusive nor independent. Since P(B|A)≠0, the events are not mutually exclusive. Because P(B|A)≠P(B), the events are not independent.

 

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