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
A game is played in which one of two players chooses a dice from a set of three die. After the first player chooses, the second player chooses a dice from the remaining two that are left. Then the two role their dice simultaneously. The player that turns up the highest number wins. In this game, however, although the dice are
"Probability Games" Web site can you play the dice roll on this web site and let me know what you learned about probabilities by playing the game.
http://www.betweenwaters.com/probab.html. Spend a few minutes playing the "Dice Roll".
Two people play a game. A single die is thrown. If the outcome is a 2 or a 3, then player A pays player B $6.00. How much should B pay A when a 1, 4, 5, or 6 is thrown so that A and B break even, on average, over many repititions of the game?
a. $2.00
b. $8.00
c. $4.00
d. $6.00
e. None of the above
When a pair of dice is rolled, the total will range from 2 (1,1) to 12 (6,6). It is a fact that some numbers will occur more frequently than others as the dice are rolled over and over.
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
1.) A taxicab was involved in a fatal hit-and-run accident at night. Two cab companies, The Green and The Blue, operate in the city. You are told that:
? 85% of the cabs in the city are Green and 15% are Blue
? A witness identified the cab as Blue
The court tested the reliability of the witness under the same c
Please help with the following problem.
Compute the probabilities for each of the following when you throw five six-handed dice.
1) What is the probability that all five have different numbers?
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
