Question

Recall Bayes' Rule P(AIB) = P(A)P(B|A) PB) Suppose 1 in 100 birds is a duck. 1 in 10 birds walks and talks like a duck (for instance, some geese walk and talk like ducks despite not being ducks) 9 out of 10 ducks walk and talk like a duck (some ducks refuse to conform. Here I am saying that the bird walks and talks like a duck, given that the bird is a duck) The probability that a bird is a duck, given that it walks and talks like a duck, is Hint: What are the events A and B? How do the statements above translate into probabilities about events? Remember to enter your answer as a decimal number between 0 and 1 inclusive.

Answer 1

P(Bird is a duck | Walk and talk like a duck)

= P(Duck and walk and talk like a duck) / P(Walk and talk like a duck)

= (1/100 * 9/10) / (1/100 * 9/10 + 99/100 * 1/10)

= 1/12

= 0.0833