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  3. HarvardX Data Science - Probability (PH125.3x)
  • 1

    Introduction to Discrete Probability

    Free

    In this chapter, you will learn about the fundamentals of discrete probability through looking at examples of sampling from an urn with and without replacement.

  • 2

    Independence and Multiplication Rule

    In this chapter, you will learn about independence, conditional probability, and the multiplication rule through examples involving draws from an urn, rolls of a die, and sports series wins.

  • 3

    The Addition Rule

    In this chapter, you will learn about the addition rule and the Monty Hall problem.

  • 4

    Continuous Probability

    In this chapter, you will learn about continuous probability through the use of examples involving the distribution of heights and IQ scores.

  • 5

    Random Variables and Sampling Models

    In this chapter, you will learn about random variables and sampling models exploring an example looking at various aspects of the game of chance American Roulette.

  • 6

    The Central Limit Theorem

    In this chapter, you will learn about the Central Limit Theorem and compare results from Monte Carlo simulations to those obtained using the Central Limit Theorem for games of chance.

  • 7

    The Big Short

    In this chapter, you will learn about interest rates and the big short.

Initializing

Exercise

Exercise 1. The Cavs and the Warriors

Two teams, say the Cavs and the Warriors, are playing a seven game championship series. The first to win four games wins the series. The teams are equally good, so they each have a 50-50 chance of winning each game.

If the Cavs lose the first game, what is the probability that they win the series?

Instructions

100 XP
  • Assign the number of remaining games to the variable n.
  • Assign a variable outcomes as a vector of possible outcomes in a single game, where 0 indicates a loss and 1 indicates a win for the Cavs.
  • Assign a variable l to a list of all possible outcomes in all remaining games. Use the rep function to create a list of n games, where each game consists of list(outcomes).
  • Use the expand.grid function to create a data frame containing all the combinations of possible outcomes of the remaining games.
  • Use the rowSums function to identify which combinations of game outcomes result in the Cavs winning the number of games necessary to win the series.
  • Use the mean function to calculate the proportion of outcomes that result in the Cavs winning the series and print your answer to the console.