and Anchor Crown and Anchor is an English dice game. The game uses a game board with six squares. Each square contains one of the following symbols: hearts, a crown, diamonds, spades, an anchor and clubs. The game is played with three dice. The dice do not contain the usual numbers 1 up until 6, but the symbols of the game board. The rules of the game are as follows: The player bets money on one of the six squares. Next, three dice are rolled. If one or more dice show the chosen symbol, the player gets his bet back plus as many times his bet as the symbol has been rolled with the dice. Suppose that 'crown, crown, clubs' is rolled. . If a player has bet his money on crown, he gets his bet back and wins his bet twice. . If a player has bet his money on clubs, he gets his bet back and wins his bet once. In all other cases, the bet is lost. . Boris bets one euro on crown. The probability of Boris losing his bet is equal to 125 216 1p a Show this using a calculation. the game board W is equal to Boris' profit in euro's. In the table below you see the probability distribution of W. Three probabilities are missing from the table. $ - Times U If a player has bet his money on clubs, he gets his bet back and wins his bet once. In all other cases, the bet is lost. Boris bets one euro on crown. The probability of Boris losing his bet is equal to 125 216 Ip a Show this using a calculation. 2p d 4pe W is equal to Boris' profit in euro's. In the table below you see the probability distribution of W. Three probabilities are missing from the table. k P(W = k) -1 125 216 1 4p b Calculate the missing probabilities and show that E(W) = -0.08 euro. 1p c Explain the meaning of the number -0.08 within the context of this question. 2 After playing the game a few times, Boris notices that the total number of times 'anchor is thrown is low compared to what you may expect. He therefore suspects that one of the dice is unfair. He decides to perform a statistical test for each of the three dice. He throws each die thirty times and counts the number of times the die shows anchor. E- 3 Give the null hypothesis and the alternative hypothesis of this statistical test. At how many times anchor (out of thirty) will Boris draw the conclusion that a die is unfair? Use a significance level of 5%. Explain your answer clearly. 1- Times