Bayes' theorem applied

Let's actually solve out a pretty straightforward, yet typical Bayes' theorem interview problem. You have two coins in your hand. Out of the two coins, one is a real coin (heads and tails) and the other is a faulty coin with tails on both sides.

You are blindfolded and forced to choose a random coin and then toss it in the air. The coin lands with tails facing upwards. Find the probability that this is the faulty coin.

This exercise is part of the course

Practicing Statistics Interview Questions in Python

Exercise instructions

Print the probability of the coin landing tails.
Print the probability of the coin being faulty.
Print the probability of the coin being faulty and landing tails.
Print and solve for the probability that the coin is faulty, given it came down on tails.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Print P(tails)
print(____)

# Print P(faulty)
print(____)

# Print P(tails and faulty)
print(____)

# Print P(faulty | tails)
print(____)

Edit and Run Code

This exercise is part of the course

Practicing Statistics Interview Questions in Python

AdvancedSkill Level

4.7+

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This chapter kicks the course off by reviewing conditional probabilities, Bayes' theorem, and central limit theorem. Along the way, you will learn how to handle questions that work with commonly referenced probability distributions.

Exercise 1: Conditional probabilities Exercise 2: Setting up problems Exercise 3: Bayes' theorem applied

Current Exercise

Exercise 4: Central limit theorem Exercise 5: Samples from a rolled die Exercise 6: Simulating central limit theorem Exercise 7: Probability distributions Exercise 8: Bernoulli distribution Exercise 9: Binomial distribution Exercise 10: Normal distribution

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Exercise 1: Descriptive statistics Exercise 2: Mean or median Exercise 3: Standard deviation by hand Exercise 4: Categorical data Exercise 5: Encoding techniques Exercise 6: Exploring laptop prices Exercise 7: Two or more variables Exercise 8: Types of relationships Exercise 9: Pearson correlation Exercise 10: Sensitivity to outliers

Prepare to dive deeper into crucial concepts regarding experiments and testing by reviewing confidence intervals, hypothesis testing, multiple tests, and the role that power and sample size play. We'll also discuss types of errors, and what they mean in practice.

Exercise 1: Confidence intervals Exercise 2: Confidence interval by hand Exercise 3: Applying confidence intervals Exercise 4: Hypothesis testing Exercise 5: One tailed z-test Exercise 6: Two tailed t-test Exercise 7: Power and sample size Exercise 8: Effect on type II error Exercise 9: Calculating sample size Exercise 10: Visualizing the relationship Exercise 11: Multiple testing Exercise 12: Calculating error rates Exercise 13: Bonferroni correction

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Exercise 1: Regression models Exercise 2: Linear regression Exercise 3: Logistic regression Exercise 4: Evaluating models Exercise 5: Regression evaluation Exercise 6: Classification evaluation Exercise 7: Missing data and outliers Exercise 8: Handling null values Exercise 9: Identifying outliers Exercise 10: Bias-variance tradeoff Exercise 11: Test and training error Exercise 12: Visualizing the tradeoff Exercise 13: Wrapping up