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? - RTA
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:
📰 You Wont Believe What HInstance Faces—HIPAA Breach Penalties Surge 10X! 📰 HIPAA Breach Penalties Hit Record Highs—Could Your Organization Be Next? 📰 Shocking HIPAA Breach Penalties Revealed: Cases You Must Avoid at All Costs! 📰 Alexnet Architecture 6343051 📰 Pelosi Tracker 9098266 📰 Parks In Reseda 5955308 📰 Bsd Nslookup Trick Explained Fix Dns Issues Faster Than Ever 2559808 📰 Jio Cinema App 8708170 📰 Spanish Of Ok Learn The Forbidden Phrases Every Native Speaks But You Dont 6890935 📰 Milan Airport Code 6541623 📰 Activated Abilities In Mtg The Ultimate Guide Thatll Supercharge Your Deck 9616290 📰 This Latest Truenews Breakthrough Shocked Millionswhy You Need To Watch Before Its Gone 4641341 📰 Native Access Download 5922614 📰 Powerbi Certification 6047526 📰 Deuce Bigalow Cast 3059680 📰 Livemixtapes 5855955 📰 Yellowstone 1923 8370434 📰 Go Out In Style The Ultimate Outfit Secret Revealed 169553Final 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
