Delayed flights

A certain airline offers flights departing to New York on Tuesdays and Fridays, but sometimes the flights are delayed:

	Delayed	On time	Total
Tuesday	24	114	138
Friday	11	127	138
Total	35	241	276

At the bottom of the Delayed column you have a total of 35, which means there were 35 delayed flights out of the total of 276 departures in the sample. Of these, 24 were on Tuesday and 11 on Friday.

Given the table, answer the following questions:

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Foundations of Probability in Python

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# Needed quantities
On_time = ____
Total_departures = ____

# Probability calculation
P_On_time = ____ / ____

print(P_On_time)

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Foundations of Probability in Python

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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

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Exercise 8: Contingency table Exercise 9: More cards Exercise 10: Total probability law Exercise 11: Formula 1 engines 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