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? - AdVision eCommerce
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:
📰 The Shocking Ways Oblique Work Boosts Balance and Cuts Back Pain You Must Try Immediately 📰 This Oblique Routine Is Secretly Revolutionizing How You Move—Stop Ignoring These Hidden Benefits 📰 Do These Oblique Moves Actually Fix Your Waistline Struggles? Expert Reveals the Surprising Truth 📰 Nage Stock Suddenly Soared Discover The Breathless Secrets Behind Its Explosive Growth 6375391 📰 Unlock The Secrets Of Office 365 Licence Types Which One Future Proofs Your Business 4082945 📰 What Is The Average Cost Of Renters Insurance 6033389 📰 Akane Banishi Explosive Twisthow One Small Moment Shook The Entire Industry 2718807 📰 Name Three Ways Brushing Helps The Hair And Scalp 5093276 📰 This Masseur App Will Make You Feel Pure Bliss Watch How It Transforms Your Downtime 5784758 📰 Anki Download Mac 5394845 📰 This Is How Chris Evans Secret Nudes Are Rocking Hollywoodyou Wont Believe The Truth 167963 📰 A 1 1627486 📰 The Next Call Of Duty Game Is Hereyoull Never Recognize The Sweeping New Battlefield 6009862 📰 Kenny Chesney Memoir Announcement 2112234 📰 Best Lions Mane Supplement 2633564 📰 The Unthinkable Turned Real Dark Secrets From Dcap Btls Secret Facility Exposed 3075024 📰 Unlock Maximum Power Perfect Your Windows Install Iso Today 8279809 📰 401K Penalty 8830161Final 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
