John's Billard Balls
Discrete Mathematics
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 \(a + b\)?
by
Calvin Lin