# Updated Final Exam Review Sheet

Early this morning I received an email from the Math Department with an updated Final Exam Review Sheet for MAT 1272.  The good news is that it is very similar to the review sheet we have been using in class – so if you can do the review sheet that I handed out, you will be mostly well prepared for the final.  However, there are two problems on the new sheet that are quite different from problems on the old sheet, #10 and #11. Here they are:

10) Of a company’s employees, 35% are women and 8% are married women.  Suppose an employee is selected at random.  Given that the selected employee is a woman, what is the probability that she is married?

ANS: 0.2286

11) A recent undergraduate student has applied to graduate schools of two universities, A and B.  The student feels that she has a 60% chance of receiving an offer from university A and a 50% chance of receiving an offer from university B.  If she receives an offer from university B, she believes that she has an 80% chance of receiving an offer from university A.
a) What is the probability that both universities will make her an offer?
b) What is the probability that at least one university will make her an offer?
c) If she receives an offer from university B, what is the probability that she will not receive an offer from university A?

ANS: a) 0.4, b) 0.7, c) 0.2

HINT:  Both of these problems rely on the formulas related to combining probabilities:

Multiplication Rule:  $P(A\: and \: B) = P(A) \cdot P(B|A)$
Addition Rule: $P(A\: or\: B) = P(A) + P(B) - P(A\: and\: B)$
Conditional Probability: $P(B|A) = \frac{P(A\: and\: B)}{P(A)}$