[6] . To help decide on a dessert for a huge family birthday dinner, the birthday girl asked each guest if they liked rocky-road ice cream, apple pie, or chocolate cake. Of her 80 disti guests, 65 guests like the ice cream, 44 guests like the pie, 42 guests like the cake, 35 the sun guests like the ice cream & the pie, 31 guests like the ice cream & the cake, 21 guests like the pie & the cake, and 15 guests like all three. best an ided. a) Represent this data using the Venn Diagram en if w given. Use the letters I, P, and C to represent the sets of guests who like ice cream, pie, and notatic cake respectively. Be sure to fill in all regions vided w of the Venn Diagram. ARK b) How many people liked ice cream, pie, wers the (45] or cake? c) How many people liked only ice cream? een a pel d) What is the probability that a guest likes pie & cake, but not ice cream? but doesn Seventy-five children were put into a corn maze at 'Fear Farm' 4 times each and the [71 [8] 7 . number of successful attempts for each child were recorded and tabulated as shown in 't in the following table. Note that the random variable X represents the number of successful attempts by a rat. tion X Frequency P(x) 0 15 30 20 3 6 4 4 a) Tabulate and graph the probability distribution for the number of successful attempts by completing the 'p(x)' column of the table and graphing your results on the grid provided (to the right of the table). Probabilities should be expressed as fractions in lowest terms, but values for the scale of your graph may be expressed as decimals. You do not need to put any titles on the graph. b) What is the expected number of successful attempts of the maze? Round your answer to one decimal place. You may use the fourth column of the table to help you calculate your answer. c) What is the probability that a randomly selected rat successfully completed the maze more than once? d) What is the probability that a randomly selected rat successfully completed the maze exactly once, given that it successfully completed the maze less than 3 times? [3] 8. Suppose that extensive research has found the