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MATH / Integers a, b, c, and d, not necessarily distinct, are chosen independently and at random from 0 to 2007, inclusive. What is the probability that ad−bc is even?

Problem

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problem

Integers aa, bb, cc, and dd, not necessarily distinct, are chosen independently and at random from 0 to 2007, inclusive. What is the probability that ad−bcad-bc is even?
Plain-text mathematical notation (without MathML)
Integers a, b, c, and d, not necessarily distinct, are chosen independently and at random from 0 to 2007, inclusive. What is the probability that ad−bc is even?
Original LaTeX notation
Integers $a$, $b$, $c$, and $d$, not necessarily distinct, are chosen independently and at random from 0 to 2007, inclusive. What is the probability that $ad-bc$ is even?

level

Level 5

type

Counting & Probability

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Source and history

task_id
3b14b93d-cb72-5f0b-9c7c-ba5e4857159e
task_key
counting~5fand~5fprobability--test--3b14b93d-cb72-5f0b-9c7c-ba5e4857159e
task_revision_id
1
config / split
counting_and_probability / test

Official source

initial import