Serena Williams made a successful first serve 67% of the time in a wimbledon finals match against her sister venus. If she continues to serve at the same rate the net time they play and serves 6 times in the first game, determine the following probabilities (assume that each serve is independent of each other)

a. all 6 serves will be in
b. exactly 4 serves will be in
c. at least 4 serves will be in

Please post work, I already know answers, thanks

Question

Serena Williams made a successful first serve 67% of the time in a wimbledon finals match against her sister venus. If she continues to serve at the same rate the net time they play and serves 6 times in the first game, determine the following probabilities (assume that each serve is independent of each other) 

a. all 6 serves will be in 
b. exactly 4 serves will be in
c. at least 4 serves will be in 

  Please post work, I already know answers, thanks

callisto · Answer

Serena's winning rate = 2/3
If she gets all 6 serves win, 
Probability = (win rate)x(win rate)x(win rate)x(win rate)x(win rate)x(win rate) = (win rate)^6 = (2/3)^6 = 62/729
Hmm, is it correct?