100 students were asked if they like chocolate, vanilla, or strawberry ice cream. The following data were collected:
- 56 like chocolate, but 21 of these like only chocolate.
- 39 like vanilla, but 11 of these like only vanilla.
- 48 like strawberry, but 17 of these like only strawberry.
- 13 do not like any of these flavors.
- 18 like all three flavors.
a) Introduce the corresponding events and create a Venn diagram for these data.
b) Given that a student likes chocolate, what is the probability he also likes strawberry?
c) Is liking chocolate independent of liking strawberry?