Binomial distribution in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Binomial PMF Calculation

What is the output of this code that calculates the probability of exactly 3 successes in 10 trials with success probability 0.5 using scipy's binom.pmf?

SciPy

from scipy.stats import binom
result = binom.pmf(3, 10, 0.5)
print(round(result, 4))

A 0.5000

B 0.2051

C 0.1172

D 0.2500

💡 Hint

Recall that binom.pmf(k, n, p) gives the probability of k successes in n trials with success probability p.

The binomial PMF for k=3, n=10, p=0.5 is approximately 0.1172. This is calculated using the formula for binomial probability mass function.

❓ data_output

intermediate

Number of Trials with Probability Above Threshold

Using scipy's binom.pmf, how many values of k (from 0 to 10) have a probability greater than 0.1 for n=10 and p=0.3?

SciPy

from scipy.stats import binom
probabilities = binom.pmf(range(11), 10, 0.3)
count = sum(p > 0.1 for p in probabilities)
print(count)

A 5

B 3

C 4

D 6

💡 Hint

Calculate probabilities for k=0 to 10 and count how many exceed 0.1.

For n=10 and p=0.3, the PMF values above 0.1 occur for k=2,3,4,5,6, totaling 5 values.

❓ visualization

advanced

Identify the Correct Binomial PMF Plot

Which option shows the correct plot of the binomial PMF for n=5 and p=0.6?

SciPy

import matplotlib.pyplot as plt
from scipy.stats import binom
import numpy as np

k = np.arange(0, 6)
pmf = binom.pmf(k, 5, 0.6)
plt.bar(k, pmf)
plt.xlabel('Number of successes')
plt.ylabel('Probability')
plt.title('Binomial PMF for n=5, p=0.6')
plt.show()

A A bar chart with highest bar at k=0 and probabilities summing to more than 1

B A line chart with decreasing values from k=0 to k=5

C A scatter plot with random points not matching binomial probabilities

D A bar chart with highest bar at k=3 and probabilities summing to 1

💡 Hint

Binomial PMF bars should sum to 1 and peak near np (here 5*0.6=3).

The binomial PMF for n=5, p=0.6 peaks at k=3 and the bars sum to 1. The correct plot is a bar chart with these properties.

🧠 Conceptual

advanced

Effect of Increasing Number of Trials on Binomial Distribution Shape

What happens to the shape of the binomial distribution when the number of trials n increases while keeping the success probability p fixed?

A The distribution becomes more symmetric and approaches a normal distribution shape

B The distribution becomes uniform across all outcomes

C The distribution becomes more skewed to the left

D The distribution becomes a single spike at k=0

💡 Hint

Think about the Central Limit Theorem and how binomial behaves for large n.

As n increases, the binomial distribution approaches a normal distribution shape, becoming more symmetric around the mean np.

🔧 Debug

expert

Identify the Error in Binomial PMF Calculation Code

What error does this code produce when trying to calculate the binomial PMF for k=3, n=10, p=0.5? from scipy.stats import binom result = binom.pmf(3, 0.5, 10) print(result)

SciPy

from scipy.stats import binom
result = binom.pmf(3, 0.5, 10)
print(result)

A ValueError because probability p is out of range

B TypeError because parameters are in wrong order

C SyntaxError due to missing parentheses

D No error, outputs correct probability

💡 Hint

Check the order of parameters for binom.pmf(k, n, p).

The parameters are in wrong order: n should be second and p third. Passing p as n causes a TypeError.