SOLUTION: Carefully explain your solutions to each of the following questions. You are at a Casino. The game you are playing is simple. You roll an ordinary pair of dice. Then you

Algebra ->  Algebra  -> Probability-and-statistics -> SOLUTION: Carefully explain your solutions to each of the following questions. You are at a Casino. The game you are playing is simple. You roll an ordinary pair of dice. Then you      Log On

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Question 342027: Carefully explain your solutions to each of the following questions.

You are at a Casino. The game you are playing is simple. You roll an ordinary pair of dice. Then you calculate the product of the two numbers on the dice. If the product is odd, you win. If the product is even, you lose. Assume that you gain $5 for every win and lose $3 for every loss.
a) What is the theoretical probability of winning the game? Show your calculations.
b) What is the theoretical probability of losing the game? Show your calculations.
c) If you played the game 12 times, how many times would you expect to win? Explain.
d) If you start with $50, how much money would expect to have after playing 12 games? Explain.
e) If you start with $300, how much money would expect to have after playing 100 games? Explain.
f) What if you start with $3000 and play until you lose all of your money, how many games do you think this would take? Explain.


Answer by stanbon(57206) About Me  (Show Source):
You can put this solution on YOUR website!
You are at a Casino. The game you are playing is simple. You roll an ordinary pair of dice. Then you calculate the product of the two numbers on the dice. If the product is odd, you win. If the product is even, you lose. Assume that you gain $5 for every win and lose $3 for every loss.
# of odd products: odd*odd = 3*3 = 9
# of even products: 36-9 = 27
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a) What is the theoretical probability of winning the game? Show your calculations. ::::: 9/36 = 1/4
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b) What is the theoretical probability of losing the game? Show your calculations.::::::: 27/36 = 3/4
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c) If you played the game 12 times, how many times would you expect to win? Explain.::::1/4 = x/12; x = 3 times
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d) If you start with $50, how much money would expect to have after playing 12 games? Explain. ::::win 3 games = $15; lose (3/4)12 = 9 games = $27
%50-12 = $38
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e) If you start with $300, how much money would expect to have after playing 100 games? Explain.
I'll leave that to you.
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f) What if you start with $3000 and play until you lose all of your money, how many games do you think this would take? Explain.
I'll leave that to you also.
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Cheers,
Stan H.