1)At a local university, the probability that a first-year student takes an Algebra class is 0.75, the probability of the student taking a Biology class is 0.40, and the probability of taking both is 0.25. Hint: Use a Venn Diagram.

a. Find the probability that the student takes at least one of the courses

b. Find the probability that the student is only taking an Algebra class.

c. Find the probability that the student is taking only one course. d. Find the probability that the student is not taking both courses.

2)A committee is formed by selecting 4 members from a group of 9 Republicans and 11 Democrats.

a. Find the probability that there are an equal number of members from each party on the committee

b. Find the probability that there is at least one member from each party on the committee.

3)The probability that a tennis player wins his next match is 8/11. What are the odds against the player winning his next match?

4)A 4-digit PIN is created from set 0, 1, 2, 3, 4, 5, 6, 7, 8. Suppose the digits are chosen randomly. Find the probability that no digit is repeated.

5) The local weatherman reports that today the probability of rain is 0.45, the probability of a tornado is 0.35, and the probability of both is 0.12. What is the probability of rain today, given there is no tornado?

6)Given Pr()= 0.60 and Pr()= 0.15.

a)Find Pr() when A and B are disjoint events.

b. Find Pr() when A and B are independent events.

7)Each morning on her way to work, a woman must pass over railroad tracks at two separate crossings along her route. The distance between the crossing is great, and the crossings operate independently of each other. The probability that a train stops the woman at the first crossing is 0.2, while the probability that she is stopped by a train at the second crossing is 0.6.

a)Find the probability that the woman stops at only one of the crossings on her way to work?