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# Probability Question Watch

1. Found out my book has answers to odd questions only... here is the question, I got 76/207.

Following is a description of the game of craps. A player rolls two dice and computes the total of the spots showing. If the player’s first toss is a 7 or an 11, the player wins the game. If the first toss is a 2, 3, or 12, the player loses the game. If the player rolls anything else (4, 5, 6, 8, 9or 10) on the first toss, that value becomes the player’s point. If the player does not win or lose on the first toss, he tosses the dice repeatedly until he obtains either his point or a 7. He wins if he tosses his point before tossing a 7 and loses if he tosses a 7 before his point. What is the probability that the player wins a game of craps?
2. (Original post by DQd)
Found out my book has answers to odd questions only... here is the question, I got 76/207.

Following is a description of the game of craps. A player rolls two dice and computes the total of the spots showing. If the player’s first toss is a 7 or an 11, the player wins the game. If the first toss is a 2, 3, or 12, the player loses the game. If the player rolls anything else (4, 5, 6, 8, 9or 10) on the first toss, that value becomes the player’s point. If the player does not win or lose on the first toss, he tosses the dice repeatedly until he obtains either his point or a 7. He wins if he tosses his point before tossing a 7 and loses if he tosses a 7 before his point. What is the probability that the player wins a game of craps?
I get 244/495.

Spoiler:
Show

8/36 in total for an initial 7 or 11.

1/36 each for a 4 or 10
25/396 each for a 5 or 9
16/360 each for a 6 or 8
Post working if you wish someone to check.
3. (Original post by ghostwalker)
I get 244/495.
Spoiler:
Show

8/36 in total for an initial 7 or 11.

1/36 each for a 4 or 10
25/396 each for a 5 or 9
16/360 each for a 6 or 8
Post working if you wish someone to check.
P of not winning or loosing is 24/36 for first throw.
I don't know how to work out the probability of winning in the 2nd throw.
Code:
```4    3/36
5    4/36
6    5/36
8    5/36
9    4/36
10   3/36```
4. (Original post by DQd)
P of not winning or loosing is 24/36 for first throw.
I don't know how to work out the probability of winning in the 2nd throw.
Code:
```4    3/36
5    4/36
6    5/36
8    5/36
9    4/36
10   3/36```
Start by considering just one case - that of winning with a "4", say.

And try a probability tree to see what's goiing on.

After the intial "4" there are only three possible actions. Can you take it from there?

PS: If not, don't just say "No". The more input you can bring to the question, the better.

Updated: October 15, 2016
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