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Omni-MATH / Two numbers a and b with 0≤a≤1 and 0≤b≤1 are chosen at random. The number c is defined by c=2a+2b. The numbers a,b and c are each rounded to the nearest integer to give A,B and C, …

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problem

Two numbers aa and bb with 0≤a≤10 \leq a \leq 1 and 0≤b≤10 \leq b \leq 1 are chosen at random. The number cc is defined by c=2a+2bc=2a+2b. The numbers a,ba, b and cc are each rounded to the nearest integer to give A,BA, B and CC, respectively. What is the probability that 2A+2B=C2A+2B=C?
Plain-text mathematical notation (without MathML)
Two numbers a and b with 0≤a≤1 and 0≤b≤1 are chosen at random. The number c is defined by c=2a+2b. The numbers a,b and c are each rounded to the nearest integer to give A,B and C, respectively. What is the probability that 2A+2B=C?
Original LaTeX notation
Two numbers $a$ and $b$ with $0 \leq a \leq 1$ and $0 \leq b \leq 1$ are chosen at random. The number $c$ is defined by $c=2a+2b$. The numbers $a, b$ and $c$ are each rounded to the nearest integer to give $A, B$ and $C$, respectively. What is the probability that $2A+2B=C$?

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Source and history

task_id
8b7616bd-7fa9-5499-87d6-be5b66002b4e
task_key
test--8b7616bd-7fa9-5499-87d6-be5b66002b4e
task_revision_id
1
config / split
/ test

Official source

initial import