Tuesday Teaser #31
A nice mixture of sports and probability this week - ideal if you ask me :)
In a straight knockout tennis tournament involving 128 players, how many matches are played? N.B. This is very easy if you think about it in the right way…
Now imagine each player is ranked 1 to 128. If the tournament bracket is selected randomly, what are the chances that the top-ranked player will play the second-ranked player in the final, if results are faithful to rankings?
If the tournament bracket is decided randomly, what is the probability that all the top 16 players will play in the Round of 16? (Again assume that the top 16 players, true to form, beat lesser-ranked opponents.) How many of the top 16 ranked players, on average, would be expected to reach the round of 16?
