### Instruction: Fifty ping-pong-balls are numbered 1, 2, 3, ..., 49, 50. A ball is chosen at random. What is the probability that the number on the selected ball is a multiple of 5 or 7 or both? Express your answer as a common fraction.### Response: I want to find the probability of a ball having a number that is a multiple of 5 or 7 or both.
This means that the number on the ball must be in the set {5, 7, 10, 14, 15, 20, 21, 25, 28, 30, 35, 40, 42, 45, 49, 50}.
There are 16 numbers in this set, out of 50 possible numbers.
Therefore, the probability of selecting such a ball is 16/50, which can be simplified by dividing both numerator and denominator by 2.
The simplified fraction is 8/25.