4 teams compete head-to-head in a sin- gle elimination tournament (with the healthiest-looking plants declared as winners). Thus, 32 games will be played in the first round, 16 in the second round, etc. with winners moving on to subsequent rounds, for a total of 63 games. There are no ties. You have been tasked with predicting a winner for each of the 63 games before the competition starts. You receive 1 point for each correctly guessed winner for the first round, with the points rewarded for each correct prediction doubling for each subsequent roundyou receive 32 points for correctly guessing the winner of the final championship match in the 6th round. There's a catch: you are an absolute gardening novice with no ability to determine the quality of the plants whatsoever, thus you've left each of your predictions to a fair coin flip, i.e. for a given match-up you pick a predicted winner with 50/50 odds.

How many points do you expect to earn? Hint: What is the probability of correctly guessing the winner of a game in round 1? round 2? What about in round n?