# Question: A single elimination tournament with four players is to be held

A single-elimination tournament with four players is to be held. A total of three games will be played. In Game 1, the players seeded (rated) first and fourth play. In Game 2, the players seeded second and third play. In Game 3, the winners of Games 1 and 2 play, with the winner of Game 3 declared the tournament winner. Suppose that the following probabilities are given:

a. Describe how you would use a selection of random digits to simulate Game 1 of this tournament.

b. Describe how you would use a selection of random digits to simulate Game 2 of this tournament.

c. How would you use a selection of random digits to simulate the third game in the tournament? (This will depend on the outcomes of Games 1 and 2.)

d. Simulate one complete tournament, giving an explanation for each step in the process.

e. Simulate 10 tournaments, and use the resulting information to estimate the probability that the first seed wins the tournament.

f. Ask four classmates for their simulation results. Along with your own results, this should give you information on 50 simulated tournaments. Use this information to estimate the probability that the first seed wins the tournament.

g. Why do the estimated probabilities from Parts (e) and (f) differ? Which do you think is a better estimate of the true probability? Explain.

a. Describe how you would use a selection of random digits to simulate Game 1 of this tournament.

b. Describe how you would use a selection of random digits to simulate Game 2 of this tournament.

c. How would you use a selection of random digits to simulate the third game in the tournament? (This will depend on the outcomes of Games 1 and 2.)

d. Simulate one complete tournament, giving an explanation for each step in the process.

e. Simulate 10 tournaments, and use the resulting information to estimate the probability that the first seed wins the tournament.

f. Ask four classmates for their simulation results. Along with your own results, this should give you information on 50 simulated tournaments. Use this information to estimate the probability that the first seed wins the tournament.

g. Why do the estimated probabilities from Parts (e) and (f) differ? Which do you think is a better estimate of the true probability? Explain.

## Answer to relevant Questions

Many fire stations handle emergency calls for medical assistance as well as calls requesting firefighting equipment. A particular station says that the probability that an incoming call is for medical assistance is .85. This ...The following data are a sample of survival times (in days from diagnosis) for patients suffering from chronic leukemia of a certain type: a. Construct a relative frequency distribution for this data set, and draw the ...Consider the variable x = time required for a college student to complete a standardized exam. Suppose that for the population of students at a particular university, the distribution of x is well approximated by a normal ...Determine the following standard normal (z) curve areas: a. The area under the z curve to the left of 1.75 b. The area under the z curve to the left of 20.68 c. The area under the z curve to the right of 1.20 d. The area ...Consider the population of all 1-gallon cans of dusty rose paint manufactured by a particular paint company. Suppose that a normal distribution with mean µ = 5 ml and standard deviation σ = 0.2 ml is a reasonable model for ...Post your question