Question: 1.21 Andre Agassi and Pete Sampras decide to play a number of games together. They play nonstop and at the end it turns out that

1.21 Andre Agassi and Pete Sampras decide to play a number of games together.

They play nonstop and at the end it turns out that Sampras won n games while Agassi m, where n>m. Assume that in fact any possible sequence of games was possible to reach this result. Let Pn,m denote the probability that from the first game until the last Sampras is always in the lead. Find 1. P2,1; P3,1; Pn,1 2. P3,2; P4,2; Pn,2 3. P4,3; P5,3; P5,4 4. Make a conjecture about a formula for Pn,m.

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