1) About 20% of the population of a large country is hopelesslyromantic. If two people are randomly selected, what is the probability both are hopelesslyromantic? What is the probability at least one is hopelesslyromantic? Assume the events are independent.

a) The probability that both will be hopelesslyromantic is ____

(b) The probability that at least one person is hopelesslyromantic is ____

2) Let the sample space be S={1,2,3,4,5,6,7,8,9,10}. Suppose the outcomes are equally likely. Compute the probability of the event E={2,3,5,7}.

P(E)=____

3) A probability experiment is conducted in which the sample space of the experiment is S={12,13,14,15,16,17,18,19,20,21,22,23}. Let event E={13,14,15,16,17,18} and event F={17,18,19,20}. List the outcomes in E and F. Are E and F mutually exclusive?

a) List the outcomes in E and F: _____