benchmarks.wiki

benchmarks.wiki / Public workspace

MMLU-Pro / 9041 / Consider the trial on which a 3 is first observed in successive rolls of a…

Problem

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

question

Consider the trial on which a 3 is first observed in successive rolls of a six-sided die. Let AA be the event that 3 is observed on the first trial. Let BB be the event that at least two trials are required to observe a 3 . Assuming that each side has probability 1/61 / 6, find (a) P(A)P(A).
Plain-text mathematical notation (without MathML)
Consider the trial on which a 3 is first observed in successive rolls of a six-sided die. Let A be the event that 3 is observed on the first trial. Let B be the event that at least two trials are required to observe a 3 . Assuming that each side has probability 1/6, find (a) P(A).
Original LaTeX notation
Consider the trial on which a 3 is first observed in successive rolls of a six-sided die. Let $A$ be the event that 3 is observed on the first trial. Let $B$ be the event that at least two trials are required to observe a 3 . Assuming that each side has probability $1 / 6$, find (a) $P(A)$.

category

math

options

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

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
9041
task_id
58a77e51-127c-535a-82de-0bbc70724d77
task_key
default--test--9041
task_revision_id
1
config / split
default / test

Official source

initial import