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Printjmc
counting and probability junior
Problem
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.
Solution
There are 10 balls whose number is divisible by 5. The balls are multiples of 7. There are 7 of these. The ball 35 is the unique ball that is a multiple of both 5 and 7.
In total, there are balls whose number is divisible by 5 or 7. The probability that a randomly selected ball will be one of these 16 is .
In total, there are balls whose number is divisible by 5 or 7. The probability that a randomly selected ball will be one of these 16 is .
Final answer
\frac{8}{25}