Exercise 4. A and B play a series - part 2

Repeat the previous exercise, but now keep the probability that team \(A\) wins fixed at p <- 0.75 and compute the probability for different series lengths. For example, wins in best of 1 game, 3 games, 5 games, and so on through a series that lasts 25 games.

This exercise is part of the course

HarvardX Data Science - Probability (PH125.3x)

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Exercise instructions

Use the seq function to generate a list of odd numbers ranging from 1 to 25.
Use the function sapply to compute the probability, call it Pr, of winning during series of different lengths.
Then plot the result plot(N, Pr).

Hands-on interactive exercise

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

# Given a value 'p', the probability of winning the series for the underdog team B can be computed with the following function based on a Monte Carlo simulation:
prob_win <- function(N, p=0.75){
      B <- 10000
      result <- replicate(B, {
        b_win <- sample(c(1,0), N, replace = TRUE, prob = c(1-p, p))
        sum(b_win)>=(N+1)/2
        })
      mean(result)
    }

# Assign the variable 'N' as the vector of series lengths. Use only odd numbers ranging from 1 to 25 games.


# Apply the 'prob_win' function across the vector of series lengths to determine the probability that team B will win. Call this object `Pr`.


# Plot the number of games in the series 'N' on the x-axis and 'Pr' on the y-axis.

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