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?

SEO Article: What Is the Probability That the Sum of Three Soil Slope Stability Measurements Is Even?

When a geotechnical engineer analyzes soil samples from three boreholes—each yielding a slope stability value from 1 to 6 (inclusive), similar to rolling a fair six-sided die—one engaging question naturally arises: What is the probability that the sum of the three measurements is even? Understanding this probability helps engineers assess consistency and risk in subsurface stability assessments.

Understanding the Problem

Understanding the Context

Each borehole produces a slope stability reading between 1 and 6, inclusive. Since the die is fair, each number from 1 to 6 has an equal probability of 1/6. The problem asks for the likelihood that the sum of three independent readings is an even number.

Mathematically, we want:

> P(sum of three numbers is even)

Because each sample is of a number from 1 to 6, we begin by analyzing the parity (odd or even nature) of each die roll.

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?

Key Insights

Step 1: Parity of Each Die Roll

The numbers 1 to 6 consist of:

Even numbers: 2, 4, 6 → 3 outcomes
Odd numbers: 1, 3, 5 → 3 outcomes

Each outcome has probability 3/6 = 1/2. So each reading independently has a 50% chance of being odd and 50% of being even.

🔗 Related Articles You Might Like:

📰 So the perpendicular bisector is vertical: 📰 Step 2: Compute midpoint and slope of side $AC$ 📰 Let $A = (0, 0)$, $C = (3, 4)$. 📰 This Full Fat Coconut Milk Will Change Your Cooking Forever Youll Never Use Light Again 📰 This Full Pokmon Dex Reveal Will Transform Your Battle Strategy Forever 📰 This Full Size Bedroom Set Is Everything You Need Dont Miss These Premium Rooms 📰 This Full Size Bunk Loft Will Transform Your Home Into A Dream Space You Never Knew You Needed 📰 This Full Size Keyboard Just Broke The Internetdont Miss Out On The Trending Key Choice 📰 This Full Size Trundle Bed Hides Space Like A Secret Fortyoull Never Guess How Space Saving It Truly Is 📰 This Fullmetal Alchemist Revelation Will Change How You Watch Every Episode Forever 📰 This Fully Grown Cavapoochon Is Taking The Internet By Stormare You Ready 📰 This Fumanchu Song Will Get You Dancing Tonight Heres Why Its The Hit Of The Week 📰 This Fun Of Games Secret Will Have You Playing All Night Longdont Miss It 📰 This Funeral Program Revealed Lifes Greatest Lessons You Havent Heard 📰 This Funimation Anime Twist Is Taking Youtube By Stormwatch Now 📰 This Funny Bunny Nail Polish Will Have You Giggling Unlock The Cutest Trend 📰 This Funny Face Meme Is Making Everyone Laugh Can You Guess The Origin 📰 This Funny Valentine Recipe Will Make Your Claim Heart Feltand Make Everyone Laugh

Final Thoughts

Step 2: Parity of the Sum

The sum of three numbers is even if:

All three numbers are even, or
Exactly two numbers are odd and one even (odd + odd + even = even + even = even)

Let’s compute the probabilities of these two cases.

Case 1: All three even

Probability = (1/2) × (1/2) × (1/2) = 1/8

Case 2: Two odd, one even

There are 3 ways this can happen (odd-odd-even, odd-even-odd, even-odd-odd)

Probability for one such combination (e.g., odd-odd-even) = (1/2) × (1/2) × (1/2) = 1/8
Total for all 3 combinations = 3 × (1/8) = 3/8