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

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(75887) (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
---------------------------------------
a) What is the theoretical probability of winning the game? Show your calculations. ::::: 9/36 = 1/4
---------------------------------------------
b) What is the theoretical probability of losing the game? Show your calculations.::::::: 27/36 = 3/4
---------------------------------------------
c) If you played the game 12 times, how many times would you expect to win? Explain.::::1/4 = x/12; x = 3 times
-----------------------------------------
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
----------
e) If you start with $300, how much money would expect to have after playing 100 games? Explain.
I'll leave that to you.
----------
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.
================================
Cheers,
Stan H.

RELATED QUESTIONS
A casino offers the following game: You bet on the outcome of a fair die. If correct, the (answered by GingerAle)

A casino offers the following game: You bet on the outcome of a fair die. If correct, the (answered by GingerAle)

Suppose that you are at a casino playing roulette. The strategy you are using is to,... (answered by ikleyn)

There are two competing proposals for the redevelopment of a piece of vacant land in... (answered by Theo)

Hi! I'm having some difficulty understanding how this question was worked out because it... (answered by Awesom3guy)

2. A certain casino claims that the commonly known phrase "The House Always Wins" does... (answered by greenestamps,ikleyn)

If a game were "fair," the payoff on a bet would be the same as the odds for the event.... (answered by edjones)

Two playing cards are dealt to you from a well-shuffled standard deck of 52 cards. If... (answered by Edwin McCravy)

Please show steps of how to solve the question. You are playing a game of chance in... (answered by Theo,math_tutor2020)