Seriously need help figuring this out! Based upon the NCAA NIT basketball tourna

Question

Seriously need help figuring this out!

Based upon the NCAA NIT basketball tournament using 32 teams.

Helpful Information:                 Games            Name of Round                       Correct Pick

                                                16                    First Round                              2 Points

                                                8                      Sweet 16                                3 Points          

                                                4                      Elite 8                                       8 Points

                                                2                      Final 4                                      20 Points

                                                1                      Championship Game               50 Points

**Seeds don’t matter, each team has the same probability of winning as any other team.

1. Calculate the total number of points you could receive if you got every selection right.

2. The maximum points that are available during each round.

3. The expected number of points that a person would get for the whole tournament.

4. How many different brackets you would have to pick in order to guarantee yourself getting all the points?

Another way that you can view this, would be, 32 people enter a room and there are 16 tables and 2 people sit at each table. So 16 tables and 2 people at each table makes a total of 32 people.

Each table, has a coin and they will flip it. You are trying to calculate and figure out who will win at each table. If you guess right you get the points for that round, if you guess wrong you don’t get the points.

After each round, we remove half of the tables and each new table will have 2 winners sitting at it. So for the second round, we will have only 8 tables and 16 winners that advanced. Each table will have 2 people sitting at it and we start the same process over until there is only one person left.

Explanation / Answer

(1)
Number of points one could receive in first round if one got every selection right = 2*16 = 32
Similarly in second round = 3 * 8 = 24
third round = 8 * 4 = 32
fourth round = 20 * 2 = 40
Final round = 50 * 1 = 50
Hence total number of points can be earned are = 32 + 24 + 32 + 40 + 50 = 178

(2)
Maximum points available during each round are
Round 1 : 32
Round 2 : 24
Round 3 : 32
Round 4 : 40
Round 5 : 50

(3)
Expected number of points that a person can get for the whole tournament = 0.5 * 178 = 89

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