Probability revised

Number Theory Level 1

Given that $a$ and $b$ are any non-negative integers such that $a$ is variable and $b$ is constant, find the probability that $a \equiv 0(\mod b)$

Clarification: $a \equiv 0(\mod b)$ implies that the remainder of $a$ is zero when divided by $b$ . E.g. $27 \equiv 0(\mod 3)$ .

\frac{1}{b}

1 0

\frac{1}{a}

2 solutions

Saksham Jain
Mar 22, 2018

We need numbers of the form $a=bq$ a and b are integers After every b integers there is 1 number which can be written as $a=bq$ Therefore probability is $\frac{1}{b}$

Braden Dean
May 31, 2018

We know that $0 \leq a \pmod{b} < b$ .
Therefore, the total amount of positive integer solutions for this inequality must be equal to $b$ .
Since we know that zero accounts for one out of all $b$ solutions,
The total probability must be equal to $\frac{1}{b}$ .

Probability revised

2 solutions

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