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Question
Two hundred patients who had either Eye surgery or Throat surgery were asked whether they were satisfied or unsatisfied regarding the result of their surgery
The follwoing table summarizes their response:
| Surgery | Satisfied | Unsatisfied | Total |
| Throat | 70 | 25 | 95 |
| Eye | 90 | 15 | 105 |
| Total | 160 | 40 | 200 |
If one person from the 200 patients is selected at random, determine the probability that person was unsatisfied given that the person had eye surgery
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Solution
Let event C: The patient was unsatisfied,
event D: The patient had a eye surgery.
Given, n(S) = 200
n(C ∩ D) = 15
∴ P(C ∩ D) = `("n"("C" ∩ "D"))/("n"("S")) = 15/200`
n(D) = 105
∴ P(D) = `105/200`
Required probability = `"P"("C"/"D")`
= `("P"("C" ∩ "D"))/("P"("D"))`
= `((15/200))/((105/200))`
= `15/105`
= `1/7`
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