In a lottery, the top cash prize was $616 million, going to three lucky winners. Players pick five different numbers from 1 to 54 and one number from 1 to 41. A player wins a minimum award of $100 by correctly matching two numbers drawn from the white balls (1 through 54) and matching the number on the gold ball (1 through 41). What is the probability of winning the minimum award?

An oil exploration company currently has two active projects, one in asia and the other in europe. let a be the event that the asian project is successful and b be the event that the european project is successful. suppose that a and b are independent events with p(a) = 0.2 and p(b) = 0.8. (a) if the asian project is not successful, what is the probability that the european project is also not successful? (b) what is the probability that at least one of the two projects will be successful? (c) given that at least one of the two projects is successful, what is the probability that only the asian project is successful? (round your answer to three decimal places.)