This is taken from Examwise Vol 2 for the 2011 L1 cert. SS02. Q1. The probability of passing an eye test for people over 70 years old is 80%, and failing is 20%. Fr people under 70 years old the rates are 95% and 5% respectively. 15% of the people tested are over 70 years old. A report is found of someone failing the test. What is the probability that they are over 70 years old? Can someone work this out for me? The reason being is I think there is an error in the answer given in the book, and I want to check it.

= 41.4% I thought we could get the same answer using tree diagram. If I try using tree diagram for this, I don’t get the same answer. Am I missing anything? Could someone demonstrate the same problem using tree diagram?

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