Question

Correct the final answers to 2 decimal places whenever appropriate.

A researcher wanted to find the types of pets that people in a city like. He then carried out a survey to ask a random sample of people if they like the three types of pets: Dogs (D), Cats (C) and Gerbils (G). Their responses are classified as Like (L) or Do not like (LC). 19% of the people like dogs, but do not like cats (i.e. P(DL ∩ CLC)= 0.19). 15% of the people like both dogs and gerbils. 6% of the people like all the three types of pets. 14% of the people do not like all the three types of pets. 59% of the people like cats. Suppose a person in the city is randomly selected.

1. Find the probability that the selected person likes all the three types of pets given that s/he likes dogs and gerbils.
2. Find the probability that the selected person like dogs but not cats and not gerbils.
3. Find the probability that the selected person likes gerbils but not dogs and not cats.
4. Find the probability that the selected person likes gerbils but not cats.

Answer 1

a. P( likes all the three types of pets given that s/he likes dogs and gerbils) = P (D∩C∩G)/(D∩G)

                                       = P(D∩C∩G) / P(D∩G) = 0.06/0.15 = 0.4

b. P( like dogs but not cats and not gerbils.) = 0.19-(0.15-0.06) = 0.10

c. P ( likes gerbils but not dogs and not cats) = 0.86-0.59-0.19 = .08

D. P( likes gerbils but not cats.) = .08 + (0.15-.06) = .17

Note : Please follow the diagrams then u will understand it will. solved area wise.