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Omni-MATH / Ana and Banana are rolling a standard six-sided die. Ana rolls the die twice,…

Problem

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problem

Ana and Banana are rolling a standard six-sided die. Ana rolls the die twice, obtaining a1a_{1} and a2a_{2}, then Banana rolls the die twice, obtaining b1b_{1} and b2b_{2}. After Ana's two rolls but before Banana's two rolls, they compute the probability pp that a1b1+a2b2a_{1} b_{1}+a_{2} b_{2} will be a multiple of 6. What is the probability that p=16p=\frac{1}{6}?
Plain-text mathematical notation (without MathML)
Ana and Banana are rolling a standard six-sided die. Ana rolls the die twice, obtaining a₁ and a₂, then Banana rolls the die twice, obtaining b₁ and b₂. After Ana's two rolls but before Banana's two rolls, they compute the probability p that a₁b₁+a₂b₂ will be a multiple of 6. What is the probability that p=(1)/(6)?
Original LaTeX notation
Ana and Banana are rolling a standard six-sided die. Ana rolls the die twice, obtaining $a_{1}$ and $a_{2}$, then Banana rolls the die twice, obtaining $b_{1}$ and $b_{2}$. After Ana's two rolls but before Banana's two rolls, they compute the probability $p$ that $a_{1} b_{1}+a_{2} b_{2}$ will be a multiple of 6. What is the probability that $p=\frac{1}{6}$?

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Source and history

task_id
0920f414-7662-502a-88fe-78e696bb3ffd
task_key
test--0920f414-7662-502a-88fe-78e696bb3ffd
task_revision_id
1
config / split
/ test

Official source

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