Formula 1 engines

Suppose that two manufacturers, A and B, supply the engines for Formula 1 racing cars, with the following characteristics:

99% of the engines from factory A last more than 5,000 km.
Factory B manufactures engines that last more than 5,000 km with 95% probability.
70% of the engines are from manufacturer A, and the rest are produced by manufacturer B.

What is the chance that an engine will last more than 5,000 km?

This exercise is part of the course

Foundations of Probability in Python

Exercise instructions

Calculate the following probabilities:
- The manufacturer is A (P_A).
- The engine lasts more than 5,000 km given that manufacturer is A (P_last5000_g_A).
- The manufacturer is B (P_B).
- The engine lasts more than 5,000 km given that manufacturer is B (P_last5000_g_B).
Use the total probability law to calculate the probability that the engine will last more than 5,000 km and store the result into P_last_5000.

Hands-on interactive exercise

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

# Needed probabilities
P_A = ____
P_last5000_g_A = ____
P_B = ____
P_last5000_g_B = ____

# Total probability calculation
P_last_5000 = ____

print(P_last_5000)

Edit and Run Code

This exercise is part of the course

Foundations of Probability in Python

IntermediateSkill Level

4.8+

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A coin flip is the classic example of a random experiment. The possible outcomes are heads or tails. This type of experiment, known as a Bernoulli or binomial trial, allows us to study problems with two possible outcomes, like “yes” or “no” and “vote” or “no vote.” This chapter introduces Bernoulli experiments, binomial distributions to model multiple Bernoulli trials, and probability simulations with the scipy library.

Exercise 1: Let’s flip a coin in Python Exercise 2: Flipping coins Exercise 3: Using binom to flip even more coins Exercise 4: Probability mass and distribution functions Exercise 5: Predicting the probability of defects Exercise 6: Predicting employment status Exercise 7: Predicting burglary conviction rate Exercise 8: Expected value, mean, and variance Exercise 9: Calculating the expected value and variance Exercise 10: Calculating the sample mean Exercise 11: Checking the result Exercise 12: Calculating the mean and variance of a sample

In this chapter you'll learn to calculate various kinds of probabilities, such as the probability of the intersection of two events and the sum of probabilities of two events, and to simulate those situations. You'll also learn about conditional probability and how to apply Bayes' rule.

Exercise 1: Calculating probabilities of two events Exercise 2: Any overlap?Exercise 3: Measuring a sample Exercise 4: Joint probabilities Exercise 5: Deck of cards Exercise 6: Conditional probabilities Exercise 7: Delayed flights Exercise 8: Contingency table Exercise 9: More cards Exercise 10: Total probability law Exercise 11: Formula 1 engines

Current Exercise

Exercise 12: Voters Exercise 13: Bayes' rule Exercise 14: Conditioning Exercise 15: Factories and parts Exercise 16: Swine flu blood test

Until now we've been working with binomial distributions, but there are many probability distributions a random variable can take. In this chapter we'll introduce three more that are related to the binomial distribution: the normal, Poisson, and geometric distributions.

Exercise 1: Normal distributions Exercise 2: Range of values Exercise 3: Plotting normal distributions Exercise 4: Within three standard deviations Exercise 5: Normal probabilities Exercise 6: Restaurant spending example Exercise 7: Smartphone battery example Exercise 8: Adults' heights example Exercise 9: Poisson distributions Exercise 10: ATM example Exercise 11: Highway accidents example Exercise 12: Generating and plotting Poisson distributions Exercise 13: Geometric distributions Exercise 14: Catching salmon example Exercise 15: Free throws example Exercise 16: Generating and plotting geometric distributions

No that you know how to calculate probabilities and important properties of probability distributions, we'll introduce two important results: the law of large numbers and the central limit theorem. This will expand your understanding on how the sample mean converges to the population mean as more data is available and how the sum of random variables behaves under certain conditions. We will also explore connections between linear and logistic regressions as applications of probability and statistics in data science.

Exercise 1: From sample mean to population mean Exercise 2: Generating a sample Exercise 3: Calculating the sample mean Exercise 4: Plotting the sample mean Exercise 5: Adding random variables Exercise 6: Sample means Exercise 7: Sample means follow a normal distribution Exercise 8: Adding dice rolls Exercise 9: Linear regression Exercise 10: Fitting a model Exercise 11: Predicting test scores Exercise 12: Studying residuals Exercise 13: Logistic regression Exercise 14: Fitting a logistic model Exercise 15: Predicting if students will pass Exercise 16: Passing two tests Exercise 17: Wrapping up