Probability question?

Question

If anyone could explain how the following is done, it would be greatly appreciated!

Suppose that there is a tennis tournament with 32 players. Players are matched in a completely random manner, and we assume that each player always has probability 1/2 of winning a match. What is the probability that two given players meet each other during the tournament?

Answer 1

for the first round there are 16 games to be played. there is a 1/16 chance the two will meet in round 1.

there is a 15/16 chance they do not meet in round 1 and a 1/4 probability that they both win in round 1 to advance to round two. If that happens then they have a 1/8 chance of meeting in round two. multiply these three probabilities to get 15/512 for the probability they meet in round two.

to meet in round three would be 15/16 not meeting in first round times 1/4 for both of them to win times, 7/8 * 1/4 to not meet in second round and both win, the product, the probability they meet in the third round is 105 / 2048 * 1/4 = 105 / 8192

to meet in the fourth round would be:
15/16 * 1/4 they don't meet in round 1 and both win
* 7/8 * 1/4 they don't meet in round 2 and both win
* 3/4 * 1/4 the don't meet in round 3 and both win
* 1/2 they meet in round 4
= 315 / 65536

to meet in the fifth and final round would be:
15/16 * 1/4 they don't meet in round 1 and both win
* 7/8 * 1/4 they don't meet in round 2 and both win
* 3/4 * 1/4 the don't meet in round 3 and both win
* 1/2 * 1/4 the don't meet in round 4 and both win
* 1 they meet in round 5
= 315 / 262144

sum all these together to get the total probability they meet during the tournament

= 1/16 + 15/512 + 105/8192 + 315/65536 + 315/262144
= 0.1106

Answer 2

You need to specify how many matches there are. the answer is definitely # of matches related. For instance, if the number of match is 0, any two given players would meet. If there are infinite many matches, they will certainly meet one another.