Question

suppose we are buying chocolate frogs and want to collect cards of luna, mcgonagall, neville, and harry, with probabilities 0.024, 0.01, 0.026, and 0.02, respectively. run a simulation of 100 to determine how many chocolate frogs you would need to buy, on average in order to collect each of these cards. show your r code below

Answer 1

The question involves using a simulation in R to find the average number of chocolate frogs one needs to buy to collect all four cards. The R code provided sets up a simulation loop and repeats the experiment 100 times to calculate the average. It takes into account the probability of each card and outputs the average number of purchases required.

Step-by-step explanation:

The student's question involves running a simulation to determine the average number of chocolate frogs needed to collect a complete set of cards.

In R, this can be accomplished by simulating the process of buying chocolate frogs until all four cards are collected and repeating this process many times to find an average.


Below is an example of R code that could be used to simulate this scenario 100 times:

set.seed(123) # For reproducibility
num_simulations = 100
results = numeric(num_simulations)

for (i in 1:num_simulations) {
collected = c(0, 0, 0, 0)
tries = 0
while (min(collected) == 0) {
tries = tries + 1
card = sample(c('Luna', 'McGonagall', 'Neville', 'Harry'), size = 1, prob = c(0.024, 0.01, 0.026, 0.02), replace = TRUE)
collected[card] = collected[card] + 1
}
results[i] = tries
}

average = mean(results)
print(average)

This code establishes a simulation loop where each iteration represents buying chocolate frogs until all four cards have been collected at least once.


The probability of each card is taken into account during the sampling process. The average number of tries is then calculated and printed as the result of the simulation.