Binomial distribution in SciPy - Mini Project: Build & Apply

Understanding Binomial Distribution with SciPy

📖 Scenario: Imagine you are a quality control analyst at a factory. You want to understand the probability of getting a certain number of defective items in a batch of products.

🎯 Goal: You will create a simple program to calculate binomial probabilities using SciPy. This will help you find the chance of getting exactly a certain number of defective items in a batch.

📋 What You'll Learn

Create a variable for the number of trials (batch size).

Create a variable for the probability of a defective item.

Use SciPy's binom.pmf function to calculate the probability of exactly k defective items.

Print the calculated probability.

💡 Why This Matters

🌍 Real World

Quality control teams use binomial distribution to estimate the chance of defective products in batches, helping to maintain product standards.

💼 Career

Data analysts and quality engineers often calculate binomial probabilities to make decisions about product quality and process improvements.

1

Set up the batch size and defective probability

Create a variable called n and set it to 10 for the batch size. Create another variable called p and set it to 0.2 for the probability of a defective item.

SciPy

# Your code here

Hint

Use simple assignment to create n and p variables.

2

Choose the number of defective items to check

Create a variable called k and set it to 3 to represent the exact number of defective items you want to find the probability for.

SciPy

n = 10
p = 0.2
# Your code here

Hint

Just assign the number 3 to the variable k.

3

Calculate the binomial probability

Import binom from scipy.stats. Then create a variable called prob and set it to the result of binom.pmf(k, n, p) to calculate the probability of exactly k defective items.

SciPy

n = 10
p = 0.2
k = 3
# Your code here

Hint

Use binom.pmf(k, n, p) to get the probability mass function value.

4

Print the probability result

Write a print statement to display the text "Probability of exactly 3 defective items:" followed by the value of prob.

SciPy

from scipy.stats import binom

n = 10
p = 0.2
k = 3

prob = binom.pmf(k, n, p)
# Your code here

Hint

Use print("Probability of exactly 3 defective items:", prob) to show the result.

Practice

1. What does the binomial distribution model in data science?

easy

A. The relationship between two continuous variables

B. The number of successes in a fixed number of independent trials with the same success probability

C. The average value of a continuous variable

D. The total sum of all outcomes in a dataset

Solution

1. Step 1: Understand the binomial distribution concept

   The binomial distribution counts how many times an event happens in a fixed number of tries, where each try has the same chance of success.

2. Step 2: Match the description to the options

   The number of successes in a fixed number of independent trials with the same success probability correctly describes this as the number of successes in fixed independent trials with the same success chance.

3. Final Answer:

   The number of successes in a fixed number of independent trials with the same success probability -> Option B

4. Quick Check:

   Binomial distribution = count of successes [OK]

Hint: Binomial counts successes in fixed tries with same chance [OK]

Common Mistakes:

• Confusing binomial with normal distribution
• Thinking it models averages or sums
• Mixing up independent trials with dependent events

2. Which of the following is the correct way to import the binomial distribution function from scipy.stats?

easy

A. import binom from scipy.stats

B. import scipy.binomial as binom

C. from scipy.stats import binom

D. from scipy import binomial

Solution

1. Step 1: Recall the correct import syntax for scipy.stats binomial

   The binomial distribution is accessed via scipy.stats as 'binom', so the correct import is 'from scipy.stats import binom'.

2. Step 2: Check each option's syntax

   from scipy.stats import binom matches the correct Python import syntax. Options A, B, and C are invalid Python import statements or incorrect module names.

3. Final Answer:

   from scipy.stats import binom -> Option C

4. Quick Check:

   Correct import = from scipy.stats import binom [OK]

Hint: Use 'from scipy.stats import binom' to import binomial [OK]

Common Mistakes:

• Using wrong module names like scipy.binomial
• Incorrect import syntax like 'import binom from ...'
• Forgetting to import from scipy.stats

3. What is the output of this code snippet?

from scipy.stats import binom
n, p = 5, 0.4
prob = binom.pmf(3, n, p)
print(round(prob, 3))

medium

A. 0.230

B. 0.345

C. 0.200

D. 0.410

Solution

1. Step 1: Understand binom.pmf parameters

   binom.pmf(k, n, p) gives the probability of exactly k successes in n trials with success chance p. Here, k=3, n=5, p=0.4.

2. Step 2: Calculate binomial probability for k=3

   Using the binomial formula or scipy, the probability is about 0.2304, rounded to 0.230.

3. Final Answer:

   0.230 -> Option A

4. Quick Check:

   binom.pmf(3,5,0.4) ≈ 0.230 [OK]

Hint: Use binom.pmf(k,n,p) for exact success probability [OK]

Common Mistakes:

• Confusing pmf with cdf
• Mixing up parameters order
• Rounding incorrectly

4. Identify the error in this code snippet:

from scipy.stats import binom
n, p = 10, 0.3
prob = binom.pmf(n, 10, p)
print(prob)

medium

A. The first argument to binom.pmf should be the number of successes, not total trials

B. The probability p should be an integer

C. The import statement is incorrect

D. The print statement is missing parentheses

Solution

1. Step 1: Check binom.pmf argument order

   binom.pmf(k, n, p) expects k = number of successes, n = number of trials, p = success probability.

2. Step 2: Analyze the code arguments

   Here, the first argument is n=10, which is total trials, not the number of successes. This is incorrect usage.

3. Final Answer:

   The first argument to binom.pmf should be the number of successes, not total trials -> Option A

4. Quick Check:

   binom.pmf(k,n,p) needs k successes first [OK]

Hint: First arg to pmf is successes, not total trials [OK]

Common Mistakes:

• Swapping k and n arguments
• Using integer for probability p
• Incorrect import or print syntax

5. You want to find the probability of getting at most 2 successes in 8 trials with success chance 0.5 using scipy. Which code snippet correctly calculates this cumulative probability?

hard

A. binom.cdf(8, 2, 0.5)

B. binom.pmf(2, 8, 0.5)

C. binom.sf(2, 8, 0.5)

D. binom.cdf(2, 8, 0.5)

Solution

1. Step 1: Understand cumulative probability for 'at most' successes

   To find probability of at most 2 successes, use cumulative distribution function (cdf) up to 2.

2. Step 2: Match correct function and parameters

   binom.cdf(2, 8, 0.5) correctly computes P(X ≤ 2) for n=8, p=0.5. Other options either use pmf (exact), sf (survival function), or wrong parameter order.

3. Final Answer:

   binom.cdf(2, 8, 0.5) -> Option D

4. Quick Check:

   Use binom.cdf(k,n,p) for P(X ≤ k) [OK]

Hint: Use binom.cdf for cumulative probability up to k [OK]

Common Mistakes:

• Using pmf instead of cdf for cumulative
• Swapping n and k parameters
• Using survival function sf for 'at most' instead of 'more than'