2. Assume that when you shoot at a target, you have an 80% chance of hitting it, and all your shots are independent of one another.Now consider a game in which you will take just 4 shots, and it costs nothing up front to play the game, but at the end the prizes and penalties are as follows:# of hits01234prize/ penaltylose $100lose $40lose $1win $1win $3A) Is this a profitable game for you to play, in the long run, and how can you tell? More specifically, how much money will you make or lose per play of the game, on average, in the long run? [Hint #1: First think, what is the Bernoulli trial here? What is the value of p? How many trials are there?] [Hint #2: Now think, can you use the Np shortcut here?]B) What is the expected number of hits each time you play the game? Do not use the Np shortcut! Write a mathematical expression and compute its value.C) Check your answer to (b) by using the Np shortcut.D) What is it about the problems in (a) and (c) that allows you to use the Np shortcut in (c) but not (a)?MathStatistics and Probability MATH 104
