# 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 resp - Mathematics and Statistics

Sum

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

#### 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

Concept: Independent Events
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