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Concept explainers
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.
X | -5 | -2 | 1 | 4 | 10 |
Probability | 0.33 | 0.27 | 0.2 | 0.13 | 0.07 |
Y | -5 | -2 | 1 | 4 | 25 |
Probability | 0.37 | 0.32 | 0.16 | 0.10 | 0.05 |
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
(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.
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