1. 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?

2. Scam Industries ULTRON 360 (U) artificial intelligence (AI) computer program has a 45% probability of passing an analytics evaluation. Amalgamated Ripoff Companys more expensive OMEGA () AI program has a 65% probability of passing the same evaluation. If these two events are independent, find the following probabilities.

a.P(both systems will pass the evaluation)P(U n ) =________________

b.P(at least one of them will pass the evaluation) P(U u ) =________________

3. A fair two-sided coin is tossed 6 times.What is the probability of tossing a head on the 6^th toss, given that the 5 preceding tosses were also heads?

4. Our classmate Hasiba Stukes is now a highly successful marketing wizard!Shes 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 shes come up with for the boards 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)

a.Construct an expected value payoff table for the two marketing plans A and B :

Marketing Plan Xsuccess Psuccess Xunsuccessful Punsuccessful

A

B

b.Determine the expected values of each marketing plan (show your work!!).

E(A) = ______________E(B) = _______________

c. Based on the expected return, which of Hasibas marketing plans should be approved by the board?

5. 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 doesnt matter)