Two friends A and B participate in a tennis competition. There are 14 other players, all 16 are of equal level of play. First couple is selected at random and in the next round the winner remains, getting an opponent at random and so on - all together 15 games to define the champion.
What is the probability that at some stage of the competition A will face B ?
Steve's solution is simpler (and easily generalizes to 2^n players) but here's another way to reason it out:
Person A can reason they have a 1/2 chance of only facing 1 person (they lose their first match) and a 1/4 chance of facing 2 people, 1/8 chance of facing 3, and f they win these three matches a 1/8 chance of facing 4.
The expected value is then 1*1/2+2*1/4+3*1/8+4*1/8=15/8 opponents.
The chance of meeting any specific 1 of the 15 opponents, say B, is (15/8)*(1/15)=1/8.
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Posted by Jer
on 2023-03-08 15:23:15 |
Another way
