An integer is chosen at random from the first 50 integers. What is the probability that the integer is <strong>NEITHER</strong> divisible by 5 <strong>NOR</strong> 9?

Explanation

There are 50 total integers. The number of integers divisible by 5 is \lfloor 50/5 \rfloor = 10. The number divisible by 9 is \lfloor 50/9 \rfloor = 5. The number divisible by both (45) is \lfloor 50/45 \rfloor = 1. By inclusion-exclusion, the amount of integers divisible by 5 or 9 is 10 + 5 - 1 = 14. The amount divisible by neither is 50 - 14 = 36. The probability is \frac{36}{50} = \frac{18}{25}.

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