Wimbledon finals

Serena Williams made a successful first serve 67% 0f the time in a Wimbledon finals match against her sister Venus, If she continues to serve at the same rate the next time they play and serves 6 times in the first game, determine the probability that:

1. all six first serves will be in.
2. at least 4 first serves will be in.

Correct result:

p6 =  0.0905
p2 =  0.687

Solution:

p=67%=67100=0.67 q=1p=10.67=33100=0.33 n=6  p6=pn=0.676=0.0905
C4(6)=(64)=6!4!(64)!=6521=15 C5(6)=(65)=6!5!(65)!=61=6 OK:4,5,6  p4=(n4) p4 q2=15 0.674 0.3320.3292 p5=(n5) p5 q1=6 0.675 0.3310.2673  p2=p4+p5+p6=0.3292+0.2673+0.0905=0.687



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