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? - IQnection
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:
📰 Discover the Cheapest Dental Clinic Near Me—Save Hundreds Without Breaking a Sweat! 📰 Get Affordable Teeth Care Today? Find the Best Cheap Dental Clinic Near You Now! 📰 Cheap Dental Clinics Near Me? Heres Where to Get Dreamy Smiles Without Paying a Fortune! 📰 Watch Machina Deus Ex Destroy The Line Between Manual Cyber Heres How 6372300 📰 Where Is Zurich 5935317 📰 Geometry Arrow Mastery Create Perfect Lines Like A Visual Genius Instantly 3566723 📰 Home Filtration Water System 3337447 📰 Could Bank Of Americas Stock Price Hit All Time High Err Maybe Notbut Heres Why Its Still Hot 6847737 📰 The Weeknds Height Revealed How It Fuels His Mythical Status In Music Fashion 2070311 📰 Does Dutch Bros Deliver 9698945 📰 This Unofficial Move In Assassins Creed Syndicate Changed The Game Forever 9823340 📰 Performing The Division Gives 4 Hours 981229 📰 Russell 2000 Chart 717826 📰 Brighton Suites Hotel 1343909 📰 Why Is Energy Transfer Stock Falling The Shocking Market Shift Youve Been Ignoring 7905632 📰 This Simple Explanation Will Change How You Think About Etfs Forever 9677113 📰 Soft Water Installation 9200191 📰 This Simple Youtube Banner Plan Sells Like Hot Cakes Black Banners Boost Clicks Instantly 3188012Final 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
