A deck of 100 cards is numbered from 1 through 100. The deck is shuffled and three cards are drawn without replacement. Let X be the value of the first card dealt, Y be the value of the second card dealt, and Z be the value of the third card dealt. Calculate P (X < Y < Z). Explain your reasoning.

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.)