## What is the probability that Team B wins at least one game?

### mathematics

##### Description

Team A and Team B are playing a seven-game series. The series is over when either team wins four games. Team A has a 60% chance of winning a game. Suppose the outcomes of the games are independent. Run Monte Carlo simulations to answer the following questions.

• 3a. What is the probability that Team B wins at least one game?

• 3b. What is the probability that Team A gets their first win in the third game?

• 3c. If Team A loses the first two games, what is the probability that they win the series?

• 3d. What is the probability that the series ends in exactly six games?

A lady claims that she can tell by tasting whether the tea or the milk is poured first to a cup. You are skeptical, and you design an experiment to test the claim. You give her 10 pairs of cups of tea: one with milk poured first, the other after. 1

• 4a. Suppose she picks 9 out of 10 correctly. Do you believe that she has indeed a special ability? If she is simply guessing at random, what is the chance that she picks correctly 9 or more cups out of 10?

do all these questions by using R programming