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? - inBeat
SEO Article: What Is the Probability That the Sum of Three Soil Slope Stability 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.
Image Gallery
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:
📰 This Simple Hack Let Me Switch Between Windows FASTER—You Wont Believe What Happens Next! 📰 Switch Between Windows Like a Pro: The Life-Changing Trick You Need TODAY! 📰 Did You Know You Can Switch Between Windows Without Missing a Beat? Heres How! 📰 Middle Back Stretches 8675956 📰 Wulf Yahoo Finance 2122079 📰 Hunchos Halal Spot 2571113 📰 How To Mail Merge In Word 424508 📰 Jk Rowling Sayings 5627340 📰 Craving Authentic Blackstone Fried Rice Heres The Recipe Thats Everyones Obsession 4704895 📰 The Undeniable Truth Behind Ralphs Wreck Wreck It Itll Blow Your Mind 8251297 📰 Hsa Vs Fsa The Ultimate Showdown You Cant Ignore In 2024 3372504 📰 A Appeal To Authority 9008141 📰 Effortlessly Elegant The Ultimate Line Dress Thats Taking Over Tiktok 2548778 📰 Cub Portal Shock You Wont Believe What Happens When You Enter 7569435 📰 Transform Your Look With Spring Twist Hair Heres The Mysterious Technique Pro Experts Are Using 1655548 📰 Wuwa Banners Are Taking Over The Ultimate Visual Download Now 4998680 📰 Anime Werewolf Secrets Youve Never Seenwatch Now For Shocking Twists 8554555 📰 Haywood Community College 9210584Final 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
