Question 3 a) The following table shows the prices of various ice cream options. Assume that the probability of a customer buying a single scoop is the same as that for a double. Also assume that each type of cone is equally likely to be chosen. Use the menu on page 13 and the different possible options for numbers of scoops and types of cones to complete the table. Ice cream options One scoop + cake cone One scoop + sugar cone Price, p ($) $4 $5 $6 $7 $8 Probability (P = p) 0.25 b) This is an example of what type of probability distribution? c) Calculate the expected value of the total price rounded to the nearest cent. d) Calculate the standard deviation of the total price, giving your answer to 4 decimal places. e) Describe what would happen to the expected value and the standard deviation of the price, if the price for each icecream option was decreased by $1. 6f) Mike orders 6 ice creams. Calculate the probability that all 6 of them are single scoop ice creams. Write your answer as a fraction. g) Calculate the probability that at least 4 of the ice creams are single scoop. Write your answer as a fraction. h) What is the exact probability that Mike orders all double scoops, given that he orders at most 3 single scoop ice creams? 7Incredible Ice Cream Number of Scoops One scoop $4 Two scoops $6 Cone cake cone - no extra charge sugar cone - no extra charge waffle cone - add $1 waffle bowl - add $2 Flavours chocolate, vanilla, strawberry, mint, swirl. banana, coconut, caramel. chocolate chip or butterscotch 13