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Omni-MATH / Marisa has two identical cubical dice labeled with the numbers…

Problem

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problem

Marisa has two identical cubical dice labeled with the numbers {1,2,3,4,5,6}\{1,2,3,4,5,6\}. However, the two dice are not fair, meaning that they can land on each face with different probability. Marisa rolls the two dice and calculates their sum. Given that the sum is 2 with probability 0.04, and 12 with probability 0.01, the maximum possible probability of the sum being 7 is pp. Compute ⌊100p⌋\lfloor 100 p\rfloor.
Plain-text mathematical notation (without MathML)
Marisa has two identical cubical dice labeled with the numbers {1,2,3,4,5,6}. However, the two dice are not fair, meaning that they can land on each face with different probability. Marisa rolls the two dice and calculates their sum. Given that the sum is 2 with probability 0.04, and 12 with probability 0.01, the maximum possible probability of the sum being 7 is p. Compute ⌊100p⌋.
Original LaTeX notation
Marisa has two identical cubical dice labeled with the numbers \(\{1,2,3,4,5,6\}\). However, the two dice are not fair, meaning that they can land on each face with different probability. Marisa rolls the two dice and calculates their sum. Given that the sum is 2 with probability 0.04, and 12 with probability 0.01, the maximum possible probability of the sum being 7 is $p$. Compute $\lfloor 100 p\rfloor$.

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Source and history

task_id
06eebd08-5318-54e0-ade3-a078162b8099
task_key
test--06eebd08-5318-54e0-ade3-a078162b8099
task_revision_id
1
config / split
/ test

Official source

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