In which three balls are selected simultaneously and randomly from a box. But assume that the box contains 8 red balls and 4 green balls. Also assume that each red ball selected pays $0.60, that each green ball selected pays $0.30, and that it costs $1.10 to play the game. A random variable XX is defined to be the net payoff for a player. How many different values are possible for the random variable XX?

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Asked Dec 18, 2019
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In which three balls are selected simultaneously and randomly from a box. But assume that the box contains 8 red balls and 4 green balls. Also assume that each red ball selected pays $0.60, that each green ball selected pays $0.30, and that it costs $1.10 to play the game. A random variable XX is defined to be the net payoff for a player. How many different values are possible for the random variable XX?

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The box contains 8 red balls and 4 green balls. Three balls are selected randomly from the box. There are four cases, all three are red balls, all three are green balls, 1 red and 2 green, 2 red and 1 green. Each red ball selected pays $0.60, each green ball pays $0.30 and it costs $1.10 to play the game. Assume that the random variable X is the net payoff for a player.

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Case (1): All three are red balls X = 3(S0.60)-$1.10 = $0.70 Case (2): All three are three balls X = 3(S0.30)– S1.10 = -S0.20 Case (3): 1 red and 2 green balls X =1(S0.60)+2(S0.30)-$1.10 = S0.10 Case (4): 2 red and 1 green balls X = 2(S0.60)+1(S0.30)-$1.10 = S0.40

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