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MMLU-Pro / 8099 / 5.3-15. Three drugs are being tested for use as the treatment of a certain…

Problem

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

question

5.3-15. Three drugs are being tested for use as the treatment of a certain disease. Let p1,p2p_1, p_2, and p3p_3 represent the probabilities of success for the respective drugs. As three patients come in, each is given one of the drugs in a random order. After n=10n=10 "triples" and assuming independence, compute the probability that the maximum number of successes with one of the drugs exceeds eight if, in fact, p1=p2=p3=0.7p_1=p_2=p_3=0.7
Plain-text mathematical notation (without MathML)
5.3-15. Three drugs are being tested for use as the treatment of a certain disease. Let p₁,p₂, and p₃ represent the probabilities of success for the respective drugs. As three patients come in, each is given one of the drugs in a random order. After n=10 "triples" and assuming independence, compute the probability that the maximum number of successes with one of the drugs exceeds eight if, in fact, p₁=p₂=p₃=0.7
Original LaTeX notation
5.3-15. Three drugs are being tested for use as the treatment of a certain disease. Let $p_1, p_2$, and $p_3$ represent the probabilities of success for the respective drugs. As three patients come in, each is given one of the drugs in a random order. After $n=10$ "triples" and assuming independence, compute the probability that the maximum number of successes with one of the drugs exceeds eight if, in fact, $p_1=p_2=p_3=0.7$

category

math

options

  1. $0.0996$
  2. $0.0889$
  3. $0.0675$
  4. $0.0278$
  5. $0.0542$
  6. $0.0750$
  7. $0.1123$
  8. $0.1257$
  9. $0.1824$
  10. $0.0384$

src

scibench-stat

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Source and history

upstream_id / Original problem ID
8099
task_id
ed8e1019-394f-5583-aff3-b0d1d3f39ab9
task_key
default--test--8099
task_revision_id
1
config / split
default / test

Official source

initial import