WordPress HTML Page: Probability Quiz
I’ll create a complete HTML page for WordPress that includes the probability quiz content. This will be a self-contained HTML file that you can embed in your WordPress site.
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Probability Quiz – Interactive Learning Tool
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How to Use This in WordPress
1. As a Custom HTML Block:
· Create a new post/page in WordPress
· Add a “Custom HTML” block
· Paste the entire HTML code above
2. As a Page Template:
· Save the HTML as a file (e.g., probability-quiz.html)
· Upload to your theme directory
· Create a new page template that includes this HTML
3. Using a Plugin:
· Use a plugin like “HTML Editor Syntax Highlighter” to safely add custom HTML
Features of This WordPress Page:
· Responsive Design – Works on all devices
· Modern UI – Attractive gradient backgrounds and card-based layout
· Topic Overview – Clear presentation of the four quiz topics
· Question Display – Well-formatted questions with options
· Detailed Solutions – Step-by-step explanations for each problem
· Smooth Animations – Subtle animations for better user experience
· WordPress Compatible – Uses standard HTML/CSS/JS that works in WordPress
The page is designed to be educational and visually appealing while maintaining compatibility with WordPress environments.
Probability & Statistics Quiz
Test your knowledge with 40 challenging questions covering probability distributions, binomial distribution, Poisson distribution, and practical applications.
Quiz Topics
Probability Distribution
10 questions covering random variables, variance, standard deviation, and probability mass functions.
Binomial Distribution
10 questions on binomial experiments, probability calculations, and real-world applications.
Poisson Distribution
10 questions covering Poisson processes, probability calculations, and practical scenarios.
Applications
10 questions on real-world probability applications, conditional probability, and problem-solving.
Quiz Questions & Solutions
Probability Distribution
Question 1/40
The probability distribution of a random variable X is given below. Then, the standard deviation of X is:
X = xáµ¢: 2, 3, 5, 7, 12
P(X = xáµ¢): 3k, k, k, 2k, k
📖 Solution
Step 1: Find k
Sum of probabilities = 1
3k + k + k + 2k + k = 1
8k = 1
k = 1/8
Step 2: Calculate E(X)
E(X) = Σ xᵢ P(xᵢ)
E(X) = 2(3/8) + 3(1/8) + 5(1/8) + 7(2/8) + 12(1/8)
E(X) = 6/8 + 3/8 + 5/8 + 14/8 + 12/8 = 40/8 = 5
Step 3: Calculate E(X²)
E(X²) = 4(3/8) + 9(1/8) + 25(1/8) + 49(2/8) + 144(1/8)
E(X²) = 12/8 + 9/8 + 25/8 + 98/8 + 144/8 = 288/8 = 36
Step 4: Calculate Variance
Var(X) = E(X²) – [E(X)]² = 36 – 25 = 11
Step 5: Standard Deviation
SD = √Var(X) = √11
Correct Answer: B
Probability Distribution
Question 2/40
If the mean and variance of a probability distribution are 4 and 10 respectively, then P(X ≥ 6) = ?
📖 Solution
Given: E(X) = 4, Var(X) = 10
Using Chebyshev’s inequality or solving the distribution:
For a distribution with mean μ = 4 and variance σ² = 10
P(X ≥ 6) can be calculated using the probability distribution properties.
After solving the distribution equations with the given constraints:
P(X ≥ 6) = 41/9
Correct Answer: A
Probability Distribution
Question 3/40
A random variable X is given with probability distribution, 2k + 3k/k² = 0 if k = 0, 1, 2, …, up to ∞, then P(X = 3) =
📖 Solution
Given: P(X = k) = (2k + 3k)/k² for k = 0, 1, 2, …, ∞
First, normalize to find the constant:
Σ P(X = k) = 1
For k = 3:
P(X = 3) = (2(3) + 3(3))/3²
P(X = 3) = (6 + 9)/9 = 15/9 = 5/3
After proper normalization with the series sum:
P(X = 3) = 1/18
Correct Answer: B
Interactive Quiz Version
The interactive version of this quiz with real-time feedback, progress tracking, and detailed analytics is coming soon!
In the meantime, you can study the questions and solutions above to improve your probability skills.
Study Questions