1. Suppose that 70% of college students like to dance, 40% like to sing, and 30% like to sing and dance. Select notation for writing the information provided. Then find the probabilities of the following events:
a. like to dance and don't like to sing;
b. don't like to dance and like to sing;
c. don't like to dance and don't like to sing;
d. like to dance or like to sing;
e. What can you say about the events in c) and d) in this problem?
2. Draw a Venn Diagram illustrating the region of interest for each of a)-d).
6. Continuing with problem 5) above. Find the probabilities of the following events:
a. like to sing given that they like to dance;
b. like to dance given that they like to sing;
c. like to sing given that they do not like to dance;
d. like to dance given that they do not like to sing.