55% of all the town's residents own a dog and 66% own a cat. Of the dog owners 46% also own a cat. If a town resident is chosen at random find: (round to 4 decimal places where possible)

Question

55% of all the town's residents own a dog and 66% own a cat. Of the dog owners 46% also own a cat. If a town resident is chosen at random find: (round to 4 decimal places where possible)

a. P(Own a Dog) = Correct

b. P(Own a Cat) = Correct

c. P(Own a Cat and a Dog) = Incorrect

d. P(Own a Dog GIVEN Own a Cat) = Incorrect

Answer 1

a. P(Own a Dog) = 0.55 Correct

b. P(Own a Cat) = 0.66Correct

c. P(Own a Cat and a Dog) = P(Own a Cat GIVEN own a dog) * P(Dog) =  0.46 * 0.55 = 0.253Incorrect

d. P(Own a Dog GIVEN Own a Cat) = P(Cat and Dog) /P(Cat) = 0.253/0.66 = 0.383 I