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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 the person was satisfied given that the person had Throat surgery.
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Solution
Let T ≡ set of people having throat surgery
E ≡ set of people having eye surgery
N ≡ set of people who were unsatisfied
Then n(T) = 95, n(E) = 105, n(N) = 40
One person is chosen from 200 persons in 200C1 = 200 ways.
∴ n(S) = 200.
It is given that person had throat surgery
∴ sample space is T for which n(T) = 95
Out of these favourable cases are 70 i.e., those who are satisfied
∴ the required probability = `70/95 = 14/19`.
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