Consider two games at a village fair, A and B. Let the gain in dollars in one play of Game A be denoted by random variable X, and let the gain in dollars in one play of Game B be denoted by random...

Consider two games at a village fair, A and B. Let the gain in dollars in one play of Game A be denoted by random variable X, and let the gain in dollars in one play of Game B be denoted by random variable Y. (A negative gain means that you receive less money back from the game than you paid to take part.)

Probability distributions for X and Y are shown below.

The results of each game are independent of each other.

(a) In one play of Game A, what is the probability of a positive gain? How about the probability of a positive gain in Game B?

(b) The expected value and the standard deviation of money gained in one play of Game A are $-0.77 and $4.24, respectively. Calculate the expected value and the standard deviation of the money gained in one play of Game B.

(c) Suppose you are contemplating making a lot of plays in Game A or Game B. To see which of these is smarter financially, you ask a friend, and he says that Game A should be your choice because your gain is more likely to be positive. Is this correct logic? Explain why or why not.