benchmarks.wiki

benchmarks.wiki / Public workspace

MMLU-Pro / 8648 / 5.4-17. In a study concerning a new treatment of a certain disease, two groups…

Problem

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

question

5.4-17. In a study concerning a new treatment of a certain disease, two groups of 25 participants in each were followed for five years. Those in one group took the old treatment and those in the other took the new treatment. The theoretical dropout rate for an individual was 50%50 \% in both groups over that 5 -year period. Let XX be the number that dropped out in the first group and YY the number in the second group. Assuming independence where needed, give the sum that equals the probability that Y≥X+2Y \geq X+2. HINT: What is the distribution of Y−X+25Y-X+25 ?
Plain-text mathematical notation (without MathML)
5.4-17. In a study concerning a new treatment of a certain disease, two groups of 25 participants in each were followed for five years. Those in one group took the old treatment and those in the other took the new treatment. The theoretical dropout rate for an individual was 50% in both groups over that 5 -year period. Let X be the number that dropped out in the first group and Y the number in the second group. Assuming independence where needed, give the sum that equals the probability that Y≥X+2. HINT: What is the distribution of Y−X+25 ?
Original LaTeX notation
5.4-17. In a study concerning a new treatment of a certain disease, two groups of 25 participants in each were followed for five years. Those in one group took the old treatment and those in the other took the new treatment. The theoretical dropout rate for an individual was $50 \%$ in both groups over that 5 -year period. Let $X$ be the number that dropped out in the first group and $Y$ the number in the second group. Assuming independence where needed, give the sum that equals the probability that $Y \geq X+2$. HINT: What is the distribution of $Y-X+25$ ?

category

math

options

  1. $0.1745$
  2. $0.3751$
  3. $0.5012$
  4. $0.3359$
  5. $0.3926$
  6. $0.2872$
  7. $0.6118$
  8. $0.4256$
  9. $0.4583$
  10. $0.2197$

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
8648
task_id
6c2e889a-abbe-515e-aeaf-a35c32900c9b
task_key
default--test--8648
task_revision_id
1
config / split
default / test

Official source

initial import