A bucket contains 50 lottery balls numbered 1-50. One is drawn at random. What is the probability that it is a multiple of 6 given that it is a 2-digit number?

The probability is 7/41.

We are looking for 
P(multiple of 6 given 2 digit) = P(2 digit & multiple of 6)/P(2 digit)

There are 7 2-digit numbers that are multiples of 6 between 1 and 50, out of 50 numbers; P(2 digit & multiple of 6) = 7/50

There are 41 2-digit numbers out of 50; P(2 digit) = 41/50

This gives us 7/50 ÷ 41/50 = 7/50 × 50/41 = 7/41