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?

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.