a. 11 P 5 ___________________
b. 11 C 5 ___________________
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:
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?
Hint: find the complementary probability 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: .
5. The following table shows the 2015 distribution of U.S. Senators by political party and gender:
For a single Senator selected at random, use the table to find the following:
Probability that Senator is male and a Democrat: = _________
Probability that Senator is male or a Democrat: = _________
Probability that Senator is male given that he is a Democrat: = _________
Are the events “Females” and “Republicans” mutually exclusive? Using probability techniques, explain your answer. “Yes” or “No” answers without explanation, even if correct, receive no credit.
* * * * * * * * * * * * *
6. From a survey involving 1000 university students, a market research company found that 610 owned laptops, 200 owned cars, and 125 owned cars AND laptops. If a student is selected at random, what is the empirical probability that the student owns neither a car nor a laptop?
7. Scam Industries’ ULTRON 360 (“U”) artificial intelligence (AI) computer program has a 45% probability of passing an analytics evaluation. Amalgamated Ripoff Company’s more expensive OMEGA (“Ω”) AI program has a 65% probability of passing the same evaluation. If these two events are independent, find the following probabilities.
P(both systems will pass the evaluation) = ________________
P(at least one of them will pass the evaluation) = ________________
8. A fair two-sided coin is tossed 6 times. What is the probability of tossing a “head” on the 6th toss, given that the 5 preceding tosses were also “heads”?
9. Our classmate Hasiba Stukes is now a highly successful marketing wizard! She’s making a marketing presentation to the board of Jussaynoe Pharmaceuticals, who want to sell the anti-math anxiety drug SHOVITALL™ to the public. Hasiba has two marketing plans she’s come up with for the board’s decision:
Plan A : a marketing plan that nets $30 million if successful (probability 0.8) and will lose $6 million if unsuccessful (probability 0.2)
Plan B : a marketing plan that nets $44 million if successful (probability 0.6) and will lose $10 million if unsuccessful (probability 0.4)
Construct an expected value payoff table for the two marketing plans A and B :
Determine the expected values of each marketing plan (show your work!!).
E(A) = ______________ E(B) = _______________
Based on the expected return, which of Hasiba’s marketing plans should be approved by the board?
10. Players of the “Zuper-Zillions” lottery in the country of Urkashizmein pay 1 bog for a ticket that lets them select 5 non-repeating numbers from 1 to 49 followed by one “Z-bolt” number between 1 and 30. The current “Zuper-Zillions” jackpot is a record 1,500,000,000 (1.5 billion) bogs. What is the probability of correctly guessing all 6 values with just one ticket? (Hint: order doesn’t matter)