# Question: Many of you probably played the game Rock Paper Scissors

Many of you probably played the game “Rock, Paper, Scissors” as a child. Consider the following variation of that game. Instead of two players, suppose three players play this game, and let us call these players A, B, and C. Each player selects one of these three items—Rock, Paper, or Scissors—independent of each other. Player A will win the game if all three players select the same item, for example, rock. Player B will win the game if exactly two of the three players select the same item and the third player selects a different item. Player C will win the game if every player selects a different item. If Player B wins the game, he or she will be paid $1. If Player C wins the game, he or she will be paid $3. Assuming that the expected winnings should be the same for each player to make this a fair game, how much should Player A be paid if he or she wins the game?

## Answer to relevant Questions

Customers arrive at the checkout counter of a supermarket at an average rate of 10 per hour, and these arrivals follow a Poisson distribution. Using each of the following two methods, find the probability that exactly 4 ...Five percent of all cars manufactured at a large auto company are lemons. Suppose two cars are selected at random from the production line of this company. Let x denote the number of lemons in this sample. Write the ...Briefly explain the concept of the mean and standard deviation of a discrete random variable. Indicate which of the following random variables are discrete and which are continuous. a. The amount of rainfall in a city during a specific month b. The number of students on a waitlist to register for a class c. The price ...Refer to the probability distribution you developed in Exercise 5.21 for the number of athletes in a random sample of two who have used illegal performance-enhancing drugs. Calculate the mean and standard deviation of x for ...Post your question