Let C be the event that a randomly chosen cancer patient has received chemotherapy. Let E be the event that a randomly chosen cancer patient has received elective surgery. Identify the answer which expresses the following with correct notation: Of all the cancer patients that have received chemotherapy, the probability that a randomly chosen cancer patient has had elective surgery.

 Let C be the event that a randomly chosen cancer patient has received chemotherapy. Let E be the event that a randomly chosen cancer patient has received elective surgery. Identify the answer which expresses the following with correct notation: Of all the cancer patients that have received chemotherapy, the probability that a randomly chosen cancer patient has had elective surgery.
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P(C|E)
 
P(E|C)
 
P(E) AND P(C)
 
P(C AND E)
Answer Explanation
Correct answer:
P(E|C)
Remember that in general, P(A|B) is read as "The probability of A given B," or equivalently, as "Of all the times B occurs, the probability that A occurs also." So in this case, the phrase "Of all the cancer patients who have received chemotherapy" can be rephrased to mean "Given that a cancer patient has received chemotherapy," so the correct answer is P(E|C).