Question

What is the probability that a randomly selected two-digit positive integer (10-99) is a perfect square or a perfect cube?

Answer 1

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If zero can not be admitted as the first digit, then there are 90 two-digit positive integers: {10, 11, 12 … 98, 99}. This set contains 6 perfect squares, {16, 25, 36, 49, 64, 81}, and 2 perfect cubes, {27, 64}. Note that 64 is already contained in the set of perfect squares, so the probability of selecting either a perfect square or perfect cube from the set of two-digit positive integers is 7/90.