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MMLU-Pro / 8870 / In the gambling game "craps," a pair of dice is rolled and the outcome of the…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

In the gambling game "craps," a pair of dice is rolled and the outcome of the experiment is the sum of the points on the up sides of the six-sided dice. The bettor wins on the first roll if the sum is 7 or 11. The bettor loses on the first roll if the sum is 2,3 , or 12 . If the sum is 4,5,64,5,6, 8,9 , or 10 , that number is called the bettor's "point." Once the point is established, the rule is as follows: If the bettor rolls a 7 before the point, the bettor loses; but if the point is rolled before a 7 , the bettor wins. Find the probability that the bettor wins on the first roll. That is, find the probability of rolling a 7 or 11 , P(7P(7 or 11)).
Plain-text mathematical notation (without MathML)
In the gambling game "craps," a pair of dice is rolled and the outcome of the experiment is the sum of the points on the up sides of the six-sided dice. The bettor wins on the first roll if the sum is 7 or 11. The bettor loses on the first roll if the sum is 2,3 , or 12 . If the sum is 4,5,6, 8,9 , or 10 , that number is called the bettor's "point." Once the point is established, the rule is as follows: If the bettor rolls a 7 before the point, the bettor loses; but if the point is rolled before a 7 , the bettor wins. Find the probability that the bettor wins on the first roll. That is, find the probability of rolling a 7 or 11 , P(7 or 11).
Original LaTeX notation
In the gambling game "craps," a pair of dice is rolled and the outcome of the experiment is the sum of the points on the up sides of the six-sided dice. The bettor wins on the first roll if the sum is 7 or 11. The bettor loses on the first roll if the sum is 2,3 , or 12 . If the sum is $4,5,6$, 8,9 , or 10 , that number is called the bettor's "point." Once the point is established, the rule is as follows: If the bettor rolls a 7 before the point, the bettor loses; but if the point is rolled before a 7 , the bettor wins. Find the probability that the bettor wins on the first roll. That is, find the probability of rolling a 7 or 11 , $P(7$ or 11$)$.

category

math

options

  1. $\frac{5}{36}$
  2. $\frac{10}{36}$
  3. $\frac{7}{36}$
  4. $\frac{8}{36}$
  5. $\frac{11}{36}$
  6. $\frac{6}{36}$
  7. $\frac{13}{36}$
  8. $\frac{12}{36}$
  9. $\frac{14}{36}$
  10. $\frac{9}{36}$

src

scibench-stat

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Source and history

upstream_id / Original problem ID
8870
task_id
4bdcb6c6-e60a-51ca-b704-b62a3de6e745
task_key
default--test--8870
task_revision_id
1
config / split
default / test

Official source

initial import