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? - Malaeb
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:
📰 Cheap Dental Clinic Near Me 📰 Cheap Dentist 📰 Cheap Dentists Near Me 📰 Nail Varnish Remover Super Glue 5549036 📰 Shocking Iphone X Release Date Countdownis It Iot 2024 Official Launch 7059868 📰 The Dark Genius Behind The Screams George Romeros Movies That Redefined Horror Forever 9769814 📰 Kirk Alyn 7227248 📰 Anora Plot 957560 📰 These Small Boobs Are Changing How Men See Confidence Forever 4707343 📰 Perhaps After How Many Months Means The Number Of Months Elapsed From Start And Since At Month 0 Its 200 150 Answer Is 0 9775474 📰 American Dollar Index 8728663 📰 The Hottest Bba Stock Going Viralmillions Are Cashin In Before The Crash 7015127 📰 417 Stunden Gerundet Auf Zwei Dezimalstellen 6853908 📰 1800 Stimulus Checks 2025 2937286 📰 A Cylindrical Tank With A Radius Of 3 Meters And A Height Of 5 Meters Is Filled With Water If 10 Of The Water Is Drained What Is The Remaining Volume Of Water In Cubic Meters 6683508 📰 Listagg In Oracle With Example 5717761 📰 Nebula Projector 5839971 📰 Live Update Qld Stock Price Jumpsis It Too Good To Be Real 2333710Final 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
