Suppose someone gives you 9 to 2 odds that you cannot roll two even numbers with the roll of two fair dice. This means you win $9.00 if you succeed and you lose $2.00 if you fail. What is the expected value of this game to you? Should you expect to win or loose the expected value in the first game? What can you expect if you play 100 times? Explain (a table will be helpful in finding the required probabilities).

1 2 3 4 5 6
1 1+1=2 1+2=3 1+3=4 1+4=5 1+5=6 1+6=7
2 2+1=3 2+2=4 2+3=5 2+4=6 2+5=7 2+6=8
3 3+1=4 3+2=5 3+3=6 3+4=7 3+5=8 3+6=9
4 4+1=5 4+2=6 4+3=7 4+4=8 4+5=9 4+6=10
5 5+1=6 5+2=7 5+3=8 5+4=9 5+5=10 5+7=11
6 6+1=7 6+2=8 6+3=9 6+4=10 6+5=11 6+6=12
A- What is the expected value of this game to you? $___
Should you expect to win (or lose) the expected value in the first game? Yes or No
B- What can you expect if you play 100 times ? $____
C- Explain this result- averaged over 100 games, you should expect to (win or lose) $___.

Solution Preview

Of the above 36 possible outcomes, 9 involve two even numbers. Thus the probability of rolling two ...

Solution Summary

The solution computes the odds of winning a game involving dice as well as our expected winnings per play.

A popular dicegame, called "craps," is played in the following manner. A player starts by rolling two dice. If the result is a 7 or 11, the player wins. If the result is 2, 3, or 12, the player loses. For any other sum appearing on the dice, the player continues to roll the dice until that outcome reoccurs (in which case th

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http://www.betweenwaters.com/probab.html. Spend a few minutes playing the "Dice Roll".

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a. $2.00
b. $8.00
c. $4.00
d. $6.00
e. None of the above

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A. Why will some numbers come up more frequently than others?
B. Each die has six sides numbered from 1 to 6. How many possible ways can a nu

Probabilities
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Please help with the following problem.
Compute the probabilities for each of the following when you throw five six-handed dice.
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2) What is the probability that at least four are the same?
3) What is the probability that exactly three are sixes?

Two fair dice are tossed, and the face on each die is observed.
a. Use a tree diagram to find the 36 sample points contained in the same space.
b. Assign probabilities to the sample points in part a.
c. Find the probability of each of the following events:
A = {3 showing on each die}
B = {sum of two numbers showing