Challenge No. 3: "Trick or Trick" is a game shop at Joy Land that offers games of luck, where for a nominal fee you get to play a game and if you win, you get to choose a prize. Their ultimate game with the grand prize of $1000 is the simplest of all. You are given a toy gun loaded with 10 small plastic bullets, and you are asked to shoot at a hanged white sheet. You get the prize if you successfully put a hole in it. The sheet is replaced with another new one after every bullet you shoot. a) How many attempts does it take a player, on average, to win the prize if the game shop is advertising a 20% chance of successfully rupturing the sheet by a shot? (1 marks) b) In one time, the employee at the shop forgot to change the sheets between each shot. A player came and asked to play the game. Will the expected number of times required to win stay the same or differ? Explain. (1 mark) c) Referring to part "a", the administration employees received many complaints that this game is rigged, and the claim that there is a 20% chance of putting a hole in the sheet is a lie. You were asked to quietly perform a field study and confirm if these claims have merit. You sat at the bench facing the game shop and started taking notes. 1. What data are you supposed to collect to expose the shop? (1 mark) ii. Explain in general terms what analysis do you need to perform on the data in order to verify the claims? (1 mark)