You've been scheduled to play three games of pickleball against someone you know very little about. Assume your opponent is either an amateur, an equal (i.e., they are just as talented as you are, but no more), or a professional. You can assume your opponent is equally likely to be any of the three levels, and that you'll win a single game against the amateur, your equal, and the professional with probabilities p1, 0.5, and p2respectively, where we'll assume that 0<p2<0.5<p1<1. Question: What is the probability of winning the first of the three games? Express your general answer in terms of p1 and p2, but you can use the answer checker to verify your answer using p1=0.7and p2=0.25 out to at least three decimal places.
You've been scheduled to play three games of pickleball against someone you know very little about. Assume your opponent is either an amateur, an equal (i.e., they are just as talented as you are, but no more), or a professional. You can assume your opponent is equally likely to be any of the three levels, and that you'll win a single game against the amateur, your equal, and the professional with probabilities p1, 0.5, and p2respectively, where we'll assume that 0<p2<0.5<p1<1.
Question: What is the probability of winning the first of the three games? Express your general answer in terms of p1 and p2, but you can use the answer checker to verify your answer using p1=0.7and p2=0.25 out to at least three decimal places.
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