Question

There are 64 teams who play in a single elimination tournament (hence 6 rounds), and you have to predict all the winners in all 63 games. Your score is then computed as follows: 32 points for correctly predicting the final winner, 16 points for each correct finalist, and so on, down to 1 point for every correctly predicted winner for the first round. (The maximum number of points you can get is thus 192.) Knowing nothing about any team, you flip fair coins to decide every one of your 63 bets. Compute the expected number of points. [1]

Answer 1

Solution:

GIVEN THAT:

There are 64 teams who play single elimination tournament,

hence 6 rounds, and you have to predict all the winners in all 63 games.

Here, to determine the expected No of points :- ECP) - 25-'xp chance =112 Ecpg) = 25-extes => 25(2-5) 25-1-% fiaman antn} => => 42 E Cpg] in mean E CPg] = 1/2 * Expectation of * can be given as E[x] - Egy Now substitute ECpg] that is e(x), then we get ECx] : [112 Egal :: E[x]: nie Given, there are 63 games so the Expected No No. of Winnings 6312 => 315 - Ecx] = 31.5

Answer 2

SOLUTION :

Expected points :

6th round (1 game) = 32 * 1/2 = 16 

5th round (2 games) = 2 * 16 *1/2 = 16 

4th round (4 games) = 4 * 8 *1/2 = 16 

3rd round (8 games) = 8 * 4 * 1/2 = 16

2nd round (16 games) = 16 * 2 * 1/2 = 16

Ist round ( 32 games) = 32 * 1 * 1/2 = 16 

Total expected  points = 16 * 6 = 96 (ANSWER).