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Suppose you ask a friend to randomly choose an integer between 1 and 10, inclusive.
What is the probability that the number will be more than 5 or odd? (Enter your probability as a fraction.)
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To find the probability that a randomly chosen integer between 1 and 10 is more than 5 or odd, we first identify the integers that satisfy these conditions. The numbers greater than 5 are 6, 7, 8, 9, and 10 (5 numbers). The odd numbers between 1 and 10 are 1, 3, 5, 7, and 9 (5 numbers). However, we need to avoid double-counting the odd numbers greater than 5 (7 and 9).

So, we have:

Using the principle of inclusion-exclusion:
Total = (Numbers > 5) + (Odd Numbers) - (Overlap)
Total = 5 + 5 - 2 = 8

The total number of integers between 1 and 10 is 10. Hence, the probability is:

So, the probability that the number will be more than 5 or odd is .