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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 following 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 the person had Throat surgery given that the person was unsatisfied.
Solution
Let event F: The patient had a throat surgery,
event G: The patient was unsatisfied.
Given, n(S) = 200
n(F ∩ G) = 25
∴ P(F ∩ G) = `(n(F ∩ G))/(n(S))`
= `25/200`
n(G) = 40
∴ P(G) = `(n(G))/(n(S))`
∴ P(G) = `40/200`
∴ Required probability = P(F/G)
= `(P(F ∩ G))/(P(G))`
= `(25/200)/(40/200)`
= `25/200 xx200/40`
= `25/40`
= `5/8`
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| Surgery | Satisfied | Unsatisfied | Total |
| Throat | 70 | 25 | 95 |
| Eye | 90 | 15 | 105 |
| Total | 160 | 40 | 200 |
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