# John's Billard Balls

Probability Level 3

John has a bag of colored billiard balls which are labeled with the numbers $1, 2, 3, 4, 5, 6$. He reaches into the bag, draws out a ball, records down the number and then places the ball back in the bag. He does this a total of 4 times (hence has 4 numbers). The probability that at least $2$ of the numbers are equal is $\frac{a}{b}$, where $a$ and $b$ are positive, coprime integers. What is the value of $a + b$?

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