Question ZU 4 pts Provide an appropriate response. A game is said to be "fair" if the expected value for winnings is 0, that is, in the long run, the player can expect to win 0. Consider the following game. The game costs $1 to play and the winnings are $5 for red, $3 for blue, $2 for yellow, and nothing for white. The following probabilities apply. What are your expected winnings? Does the game favor the player or the owner? Outcome | Probability Red .02 Blue .04 Yellow .16 White 78 D Question 21 4 pts Provide an appropriate response. A gambler claimed that he had loaded a die so that it would hardly ever come up 1. He said the outcomes of 1, 2, 3, 4, 5, 6 would have probabilities 1 1111 1 20,' 6 6 6' 6' 6 respectively. Can he do what he claimed? Why or why not? Is a probability distribution described by listing the outcomes along with their corresponding probabilities? Why or why not? Question 25 4 pts Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied. x P(x) 0 0.346 0.055 2 -0.092 3 0.185 4 0.083 0.423