March Madness Bracket

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Students will answer five short items applying numeric probability and basic statistical thinking to March Madness bracket scenarios. Questions include percentage conversion, expected value of upsets, independence vs. dependence, complements, and updating probabilities after an elimination. Students should show their reasoning where applicable.

YOUR PREDICTIONS

1

Add the names of the 64 teams paired up for the first round of the NCAA Men's March Madness Tournament.

1

Add the names of the teams you think will make it to the round of 32 and their pairings.

1

Add the names of the teams you think will make it to the Sweet Sixteen and their pairings.

1

Add the names of the teams you think will make it to the Elite Eight and their pairings.

1

THE RESULTS

1

Add the names of the teams that actually made it to the round of 32 and their pairings.

1

Add the names of the teams that actually made it to the Sweet Sixteen and their pairings.

1

Add the names of the teams that actually made it to the Elite Eight and their pairings.

1

Add the names of the teams that actually made it to the Final Four and their pairings.

1

THE MATH

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1

An analyst estimates that a 3-seed has a $0.65$ chance of beating a 14-seed in a first-round game. What is the probability (as a percentage) that the 3-seed wins that game?

35%

50%

65%

75%

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1

There are 32 first-round games. If each game independently has a $0.20$ probability of an upset (a lower-seeded team beating a higher-seeded team), what is the expected number of upsets in the first round? Give your answer as a number.

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1

Consider two different first-round games on the same day, Game A and Game B. Which TWO statements are true? (Choose two.)

If Game A and Game B are independent, then $P(\text{both upset}) = P(\text{upset}_A)\times P(\text{upset}_B)$.

If Team X unexpectedly beats a top seed in Game A, the probability Team Y wins Game B always increases.

If the events are dependent, knowing the result of Game A can change the probability of the outcome in Game B.

If $P(\text{upset in one game}) = 0.3$, then the expected number of upsets for that one game is $1.3$.

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1

In a bracket, the probability that a given team does not win a particular game is called its _____. (Three words or less.)

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1

Suppose you predicted a team had a $0.05$ chance to win the whole tournament before the games began. That team loses in the first round. In one short paragraph, explain numerically and conceptually how your tournament probability estimates should change after that result.

March Madness Bracket

Add the names of the 64 teams paired up for the first round of the NCAA Men's March Madness Tournament.

Add the names of the teams you think will make it to the round of 32 and their pairings.

Add the names of the teams you think will make it to the Sweet Sixteen and their pairings.

Add the names of the teams you think will make it to the Elite Eight and their pairings.

Add the names of the teams that actually made it to the round of 32 and their pairings.

Add the names of the teams that actually made it to the Sweet Sixteen and their pairings.

Add the names of the teams that actually made it to the Elite Eight and their pairings.

Add the names of the teams that actually made it to the Final Four and their pairings.

An analyst estimates that a 3-seed has a $0.65$ chance of beating a 14-seed in a first-round game. What is the probability (as a percentage) that the 3-seed wins that game?

There are 32 first-round games. If each game independently has a $0.20$ probability of an upset (a lower-seeded team beating a higher-seeded team), what is the expected number of upsets in the first round? Give your answer as a number.

Consider two different first-round games on the same day, Game A and Game B. Which TWO statements are true? (Choose two.)

In a bracket, the probability that a given team does not win a particular game is called its _____. (Three words or less.)

Suppose you predicted a team had a $0.05$ chance to win the whole tournament before the games began. That team loses in the first round. In one short paragraph, explain numerically and conceptually how your tournament probability estimates should change after that result.

Add the names of the 64 teams paired up for the first round of the NCAA Men's March Madness Tournament.

Add the names of the teams you think will make it to the round of 32 and their pairings.

Add the names of the teams you think will make it to the Sweet Sixteen and their pairings.

Add the names of the teams you think will make it to the Elite Eight and their pairings.

Add the names of the teams you think will make it to the Final Four and their pairings.

Add the two teams you think will make it to the National Championship.

Add the team you think will win the NCAA Men's March Madness tournament this year.

Add the names of the teams that actually made it to the round of 32 and their pairings.

Add the names of the teams that actually made it to the Sweet Sixteen and their pairings.

Add the names of the teams that actually made it to the Elite Eight and their pairings.

Add the names of the teams that actually made it to the Final Four and their pairings.

Add the names of the teams that actually made it to the National Championship.

Add the team that actually won the NCAA Men's March Madness tournament this year.

An analyst estimates that a 3-seed has a $0.65$ chance of beating a 14-seed in a first-round game. What is the probability (as a percentage) that the 3-seed wins that game?

There are 32 first-round games. If each game independently has a $0.20$ probability of an upset (a lower-seeded team beating a higher-seeded team), what is the expected number of upsets in the first round? Give your answer as a number.

Consider two different first-round games on the same day, Game A and Game B. Which TWO statements are true? (Choose two.)

In a bracket, the probability that a given team does not win a particular game is called its _____. (Three words or less.)

Suppose you predicted a team had a $0.05$ chance to win the whole tournament before the games began. That team loses in the first round. In one short paragraph, explain numerically and conceptually how your tournament probability estimates should change after that result.

Add the names of the teams you think will make it to the Final Four and their pairings.

Add the two teams you think will make it to the National Championship.

Add the team you think will win the NCAA Men's March Madness tournament this year.

Add the names of the teams that actually made it to the National Championship.

Add the team that actually won the NCAA Men's March Madness tournament this year.