We choose a number from the set {10,11,12,...,99} uniformly at random. (a) Let X be the first digit and Y the second digit of the chosen number. Show that X and Y are independent random variables. (b) Let X be the first digit of the chosen number and Z the sum of the two digits. Show that X and Z are not independent.

Sandy is upgrading her internet service. fast internet charges $20 for installation and $52.45 per month. quick internet has free installation but charges $57.45 per month. part 1 out of 2 complete the equation that can be used to find the number of months after which the internet service would cost the same. use the variable x to represent the number of months of internet service purchased.

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.)

The distance a bicycle travels with each turn of its wheels is about 3 1/7 times the tire diameter. the tires on mike’s bicycle have a diameter of 24 1/2 inches. how far does it travel with each turn of the wheels?