Question

Problem 2: Conditional Probabilities Julie's dog went missing after she visited the park near the woods for a picnic. Her friends had the following things to say. . Alice: "It must have gone home." . Bob: "It is probably digging for a bone somewhere in the garden." Carol: "It might have wandered off into the woods." The probability of Alice being right is 1/2. Bob can be right with probability 1/s and Carol has a 1/6 chance of being right. Julie and Alice go back to the park to search for the dog while Bob and Carol search the woods. If it is in the park, it will be found with 80% chance. In the woods, it can only be found with a 20% chance. (i) What is the probability that the dog will be found in the woods? (ii) What is the probability that the dog is lost?

Answer 1

(i) P(god will be found in woods) = P(Carol is right) x P(finding dog if its in the woods)

= (1/6) x 0.2

= 0.0333

(ii) P(dog is lost) = P(Bob is right and the dog is not found in the garden) + P(Carol is right and the dog is not found in the Woods)

= (1/3)x(1 - 0.8) + (1/6)x(1 - 0.2)

= 0.2