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MMLU-Pro / 8195 / Assuming we are underground, and the only thing we can observe is whether a…

Problem

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question

Assuming we are underground, and the only thing we can observe is whether a person brings an umbrella or not. The weather could be either rainy or sunny. Assuming the P(rain)=0.6 and P(sunny)=0.4. Assuming the weather on day kk is dependent on the weather on day k−1k-1. We can write the transition probability as P(sunny ∣\mid sunny) = P(rain ∣\mid rain) = 0.7. The person has 60\% chance to bring an umbrella when the weather is rainy, and 40\% chance to bring an umbrella when the weather is sunny, i.e. P(umbrella ∣\mid rain) = 0.6 and P(umbrella ∣\mid sunny) = 0.4. If we observe that the person (1) brought an umbrella on day 1, (2) did not bring an umbrella on day 2, (3) brought an umbrella on day 3, (4) did not bring an umbrella on day 4. What are the most likely weather from day 1 to day 4? Return the answer as a list of binary values, where 1 represents rain and 0 represents sunny.
Plain-text mathematical notation (without MathML)
Assuming we are underground, and the only thing we can observe is whether a person brings an umbrella or not. The weather could be either rainy or sunny. Assuming the P(rain)=0.6 and P(sunny)=0.4. Assuming the weather on day k is dependent on the weather on day k−1. We can write the transition probability as P(sunny ∣ sunny) = P(rain ∣ rain) = 0.7. The person has 60\% chance to bring an umbrella when the weather is rainy, and 40\% chance to bring an umbrella when the weather is sunny, i.e. P(umbrella ∣ rain) = 0.6 and P(umbrella ∣ sunny) = 0.4. If we observe that the person (1) brought an umbrella on day 1, (2) did not bring an umbrella on day 2, (3) brought an umbrella on day 3, (4) did not bring an umbrella on day 4.  What are the most likely weather from day 1 to day 4? Return the answer as a list of binary values, where 1 represents rain and 0 represents sunny.
Original LaTeX notation
Assuming we are underground, and the only thing we can observe is whether a person brings an umbrella or not. The weather could be either rainy or sunny. Assuming the P(rain)=0.6 and P(sunny)=0.4. Assuming the weather on day $k$ is dependent on the weather on day $k-1$. We can write the transition probability as P(sunny $\mid$ sunny) = P(rain $\mid$ rain) = 0.7. The person has 60\% chance to bring an umbrella when the weather is rainy, and 40\% chance to bring an umbrella when the weather is sunny, i.e. P(umbrella $\mid$ rain) = 0.6 and P(umbrella $\mid$ sunny) = 0.4. If we observe that the person (1) brought an umbrella on day 1, (2) did not bring an umbrella on day 2, (3) brought an umbrella on day 3, (4) did not bring an umbrella on day 4.  What are the most likely weather from day 1 to day 4? Return the answer as a list of binary values, where 1 represents rain and 0 represents sunny.

category

math

options

  1. [1, 1, 0, 0]
  2. [0, 0, 0, 0]
  3. [0, 1, 0, 0]
  4. [1, 0, 1, 1]
  5. [0, 0, 1, 1]
  6. [1, 0, 0, 1]
  7. [1, 0, 1, 0]
  8. [0, 1, 0, 1]
  9. [0, 1, 1, 0]
  10. [1, 1, 1, 1]

src

theoremQA-Math

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Source and history

upstream_id / Original problem ID
8195
task_id
2178af9e-a656-5be8-9989-ecb1d1e5901e
task_key
default--test--8195
task_revision_id
1
config / split
default / test

Official source

initial import