2. An American roulette wheel contains 38 numbers: 18 are red, 18 are black, and 2 are green. When the roulette wheel is

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2. An American roulette wheel contains 38 numbers: 18 are red,18 are black, and 2 are green. When the roulette wheel is spun, theball is equally likely to land on any of the 38 numbers. If theball lands on a black number, the player wins $8; otherwise, theplayer wins $3. The player pays $6 to play each game. Let X be theamount the player gains or loses per game. (Hint: use a negativenumber for X to represent a loss.)
a) Construct the probability distribution for the randomvariable X