Question
What is the probability that a randomly chosen two-digit
positive integer is a multiple of 5?Solution
Let's calculate the probability step by step using the Counting Method: Step 1: Count the multiples of 5 within the range of two-digit positive integers (from 10 to 99). The multiples of 5 in this range are: 10, 15, 20, 25, ..., 95. To find the number of terms in this sequence, you can use the formula for the nth term of an arithmetic sequence: nth term = first term + (n - 1) × common difference. Here, the first term (a) is 10, and the common difference (d) is 5. We want to find the nth term equal to 95. 95 = 10 + (n - 1) × 5. Now, solve for n: 95 - 10 = (n - 1) × 5, 85 = 5(n - 1). Divide both sides by 5: 85 / 5 = n - 1, 17 = n - 1. Now, add 1 to both sides: 17 + 1 = n, 18 = n. total number =99-10+1=90 Required probality will be = (18/90) = 1/5 or 0.2
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