They play until one wins the best of five sets (first to win 3 sets, wins the match). Write out the formula you use and/or the numbers you plug into your calculator.
a.) What is the probability that Federer wins exactly zero sets?
b.) What is the probability that Federer wins at least one set?
c.) What is the probability that Nadal wins at most two sets?
d.) What is the probability that Nadal wins the match, given that he loses the first set?
Probability of Federer wining a set is 0.60 Probability of Federer losing a set is =1-0.6 = 0.4
a.) probability that Federer wins exactly zero sets = 0.4*0.4*0.4*0.4*0.4 = 0.01024 b.) probability that Federer wins at least one set = 1- 0.01024 = 0.98976 C.) probability that Nadal wins at most two sets = Probability of Federer losing at most 2 set. =Probability of Federer losing 0 set + Probability of Federer losing 1 set + Probability of Federer losing 2 set = 0.6^5 + 0.4*0.6^4 + 0.4^2*0.6^3 = 0.16416
d.) probability that Nadal wins the match, given that he loses the first set = losing first set and wining 3 out of remaining 4 sets = 0.6*4C3*0.4*0.4*0.4*0.6 = 0.09216