The letters {a, b, c, d, e, f, g} are put in a random order. Each permutation is equally likely. Define the following events: A: The letter b falls in the middle (with three before it and three after it) B: The letter c appears to the right of b, although c is not necessarily immediately to the right of b. For example, "agbdcef" would be an outcome in this event. C: The letters "def" occur together in that order (e. g. "gdefbca") (a) Calculate the probability of each individual event. That is, calculate p(A), p(B), and p(C). (b) What is p(A|C)? (c) What is p(B|C)? (d) What is p(A|B)? (e) Which pairs of events among A, B, and C are independent?

Samson is going shopping for sugar and butter to make three different kinds of cookies: lemon bars, peanut butter cookies, and sugar cookies. the recipe for lemon bars calls for 2 cups of flour, 2 cups of sugar, and 1 stick of butter. the peanut butter cookie recipe calls for 2 cups of flour, 4 cup of sugar and 2 stick of butter. the sugar cookie recipe calls for 1 cup of flour, 2 cups of sugar, and 2 sticks of butter. sampson has 13 cups of flour at home, and he buys 12 cups (6 pounds) of sugar and 10 sticks of butter. how many batches of each type of cookie can he make? samson can make batches of lemon bars, batches of peanut butter cookies, and batches of 09 cookies submit reset