benchmarks.wiki

benchmarks.wiki / Public workspace

MMLU-Pro / 8098 / A typical roulette wheel used in a casino has 38 slots that are numbered …

Problem

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

question

A typical roulette wheel used in a casino has 38 slots that are numbered 1,2,3,…,36,0,001,2,3, \ldots, 36,0,00, respectively. The 0 and 00 slots are colored green. Half of the remaining slots are red and half are black. Also, half of the integers between 1 and 36 inclusive are odd, half are even, and 0 and 00 are defined to be neither odd nor even. A ball is rolled around the wheel and ends up in one of the slots; we assume that each slot has equal probability of 1/381 / 38, and we are interested in the number of the slot into which the ball falls. Let A={0,00}A=\{0,00\}. Give the value of P(A)P(A).
Plain-text mathematical notation (without MathML)
 A typical roulette wheel used in a casino has 38 slots that are numbered 1,2,3,…,36,0,00, respectively. The 0 and 00 slots are colored green. Half of the remaining slots are red and half are black. Also, half of the integers between 1 and 36 inclusive are odd, half are even, and 0 and 00 are defined to be neither odd nor even. A ball is rolled around the wheel and ends up in one of the slots; we assume that each slot has equal probability of 1/38, and we are interested in the number of the slot into which the ball falls. Let A={0,00}. Give the value of P(A).
Original LaTeX notation
 A typical roulette wheel used in a casino has 38 slots that are numbered $1,2,3, \ldots, 36,0,00$, respectively. The 0 and 00 slots are colored green. Half of the remaining slots are red and half are black. Also, half of the integers between 1 and 36 inclusive are odd, half are even, and 0 and 00 are defined to be neither odd nor even. A ball is rolled around the wheel and ends up in one of the slots; we assume that each slot has equal probability of $1 / 38$, and we are interested in the number of the slot into which the ball falls. Let $A=\{0,00\}$. Give the value of $P(A)$.

category

math

options

  1. $\frac{1}{19}$
  2. $\frac{1}{76}$
  3. $\frac{20}{38}$
  4. $\frac{2}{38}$
  5. $\frac{3}{38}$
  6. $\frac{4}{38}$
  7. $\frac{36}{38}$
  8. $\frac{1}{38}$
  9. $\frac{1}{2}$
  10. $\frac{18}{38}$

src

scibench-stat

Discussion

Discussion

No discussion posts on this page yet. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.

Source and history

upstream_id / Original problem ID
8098
task_id
2f6f1c10-edf5-51fb-b9f1-03992257ecf7
task_key
default--test--8098
task_revision_id
1
config / split
default / test

Official source

initial import