100 students are asked what pets they like from a choice of cats, dogs and hamsters.
The results are as follows.
60 like cats
64 like dogs
61 like hamsters
34 like cats and dogs
46 like dogs and hamsters
43 like cats and hamsters
32 like cats, dogs and hamsters
a)Represent this information on a Venn diagram.
Find the number of students who
(i) like dogs only;
(ii) like both dogs and cats but not hamsters;
(iii) do not like pets.
A student is randomly chosen from this group of 100 students.
c)Calculate the probability that this student likes only two kinds of pets.
d)Calculate the probability that this student likes only dogs, given that this student only likes one kind of pet.
