Two hundred patients who had either hip surgery or knee surgery were asked whether they were satisfied or dissatisfied regarding the result of their surgery. Out of the 95 that had knee surgery, 70 were satisfied. Out of the 105 that had hip surgery, 15 were dissatisfied. If one person from the 200 patients is selected at random, what is the probability that the person had knee surgery given that they were dissatisfied?Question 7Select one:a.1/4b.1/8c.3/8d.5/8
Question
Two hundred patients who had either hip surgery or knee surgery were asked whether they were satisfied or dissatisfied regarding the result of their surgery. Out of the 95 that had knee surgery, 70 were satisfied. Out of the 105 that had hip surgery, 15 were dissatisfied. If one person from the 200 patients is selected at random, what is the probability that the person had knee surgery given that they were dissatisfied?Question 7Select one:a.1/4b.1/8c.3/8d.5/8
Solution
To solve this problem, we first need to find out how many people were dissatisfied in total. We know that 15 out of 105 people who had hip surgery were dissatisfied. However, we don't know how many people who had knee surgery were dissatisfied. We do know that 70 out of 95 people who had knee surgery were satisfied, so that means 95 - 70 = 25 people who had knee surgery were dissatisfied.
So, the total number of people who were dissatisfied is 15 (from the hip surgery group) + 25 (from the knee surgery group) = 40 people.
The question asks for the probability that a person had knee surgery given that they were dissatisfied. This means we want to know out of the people who were dissatisfied, how many had knee surgery. We know that 25 people who had knee surgery were dissatisfied.
So, the probability is the number of dissatisfied knee surgery patients divided by the total number of dissatisfied patients, which is 25/40 = 0.625 or 5/8.
So, the answer is d. 5/8.
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