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Craps is a dice game in which two fair dice are cast. If
Chapter 5, Problem 8CT(choose chapter or problem)
Problem 8CT
Craps is a dice game in which two fair dice are cast. If the roller shoots a 7 or 11 on the first roll, he or she wins. If the roller shoots a 2, 3, or 12 on the first roll, he or she loses.
(a) Compute the probability that the shooter wins on the first roll. Interpret this probability.
(b) Compute the probability that the shooter loses on the first roll. Interpret this probability.
Questions & Answers
QUESTION:
Problem 8CT
Craps is a dice game in which two fair dice are cast. If the roller shoots a 7 or 11 on the first roll, he or she wins. If the roller shoots a 2, 3, or 12 on the first roll, he or she loses.
(a) Compute the probability that the shooter wins on the first roll. Interpret this probability.
(b) Compute the probability that the shooter loses on the first roll. Interpret this probability.
ANSWER:
Solution :
Step 1 of 2:
From the given information we know that the roller shoots a 2, 3, or 12 on the first roll, he or she loses.
Here two dice rolls, table for possible events.
Then the table is given below,
|
Dice 1 2 |
1 |
2 |
3 |
4 |
5 |
6 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
From the above table 2, 3 or 12 in square table and 11 or 7 is marked.
a). We know that from the above table we marked the number of 7 is 6 and the number of 11 is 1.
The probability that the shooter wins on the first roll is
P(7 or 11) =
P(7 or 11) =
P(7 or 11) = 0.2222
Therefore, the probability that the shooter wins on the first roll is 0.2222.
Here if the die are thrown 100 times, then we would expect the player will win on the first roll about 22 times.