1. Evaluate

a.) 11P5

b.) 11C5

2. What is the probability of someone correctly guessing your social security number on the first attempt? (Assume all digits 0-9 are available for use) (hint: does order matter?)

3. A jar contains 7 red, 9 white, and 8 blue marbles. If a single marble is chosen at random, find the probability that the randomly chosen marble is:

a.) red P(red)=

b.) white P(white)=

c.)Blue or red P(blue or red)=

4. Multiple Choice: An assembly plant produces 40 lawn mowers; of those, 7 are defective. Prior to shipping the mowers to retailers, the company's quality control department selects 10 of the 40 mowers at random for testing. The assembly plant will be shut down for troubleshooting if 1 or more mowers in the sample are found to be defective. what is the probability that the plant will be shut down? Justify your answer.

Hint: find the complementary probability P(E^C) or P(E') that 0 of the 10 lawn mowers selected out of the production lot of 40 (with its 7 defective mowers) are defective. The probability that plant shuts down if 1 or more mowers in sample are found defective: P(E)=1-P(E^C).

a. 0.1092 C. 0.8250

b. 0.1750 d. 0.8908

5. The following table shows the 2015 distribution of U.S. Senators by political party and gender:

Males(M) Females(F) Total

Democrats(D) 30 14 44

Republicans(R) 48 6 54

Independents(I) 2 0 2

Totals 80 20 100

For a single Senator selected at random, use the table to find the following:

a. Probability that Senator is male and a Democrat: P(Mn D)=

b. Probability that Senator is male or a Democrat: P(M U D)=

c. Probability that Senator is male given that he is a Democrat: P(M|D)=

d. Are the events "Females" and "Republicans" mutually exclusive? using probability techniques, explains your answer. "Yes" or "no" answers without explanation, evenif correct, receive no credit.