Suppose you are testing someone to see whether he or she can tell butter from margarine when it is spread on toast. you use many bite-sized pieces selected randomly, half from buttered toast and half from toast with margarine. the taster is blindfolded. the null hypothesis is that the taster is just guessing and should get about half right. when you reject the null hypothesis when it is actually true, that is often called the first kind of error. the second kind of error is when the null is false and you fail to reject. report the first kind of error and the second kind of error.

Afriend of mine is giving a dinner party. his current wine supply includes 10 bottles of zinfandel, 8 of merlot, and 11 of cabernet (he only drinks red wine), all from different wineries. (a) if he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? ways (b) if 6 bottles of wine are to be randomly selected from the 29 for serving, how many ways are there to do this? ways (c) if 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? ways (d) if 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (round your answer to three decimal places.) (e) if 6 bottles are randomly selected, what is the probability that all of them are the same variety? (round your answer to three decimal places.)