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Home » We are selecting 5 buses from a total of $ 6 + 4 + 5 = 15 $ buses. - Redraw

We are selecting 5 buses from a total of $ 6 + 4 + 5 = 15 $ buses. - Redraw

📅 May 6, 2026 👤 scraface

May 06, 2026

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📌 Question: A geotechnical engineer is analyzing soil samples from three different boreholes, each sample returned a measurement of slope stability ranging from 1 to 6 (inclusive), like a die roll. What is the probability that the sum of the three measurements is even?

📌 Solution: Each die roll (measurement) results in an integer from 1 to 6, each with equal probability. The total number of outcomes is:

📌 We now count the number of outcomes where the sum of the three numbers is even. A sum is even if there are an even number of odd numbers in the sum (i.e., 0 or 2 odd numbers).

📌 The odd numbers from 1 to 6 are: 1, 3, 5 (3 options), and the even numbers are: 2, 4, 6 (3 options).

📌 Case 1: All three numbers are even.

📌 Each number has 3 choices (2, 4, 6):

📌 3^3 = 27 \text{ outcomes}

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