From the information below the games is over in 3 sets. For Gina to win the match there are 3 possibilities.
1) Gina wins the first 2 sets with probability [tex] (\frac{2}{5} )^2 [/tex]
2)Gina wins the first set. Looses the next set. Wins the third set. [tex] (\frac{2}{5} ) (\frac{3}{5} ) (\frac{2}{5} ) [/tex]
3)Gina looses the first set. Wins the next 2 sets. [tex] (\frac{3}{5} ) (\frac{2}{5} ) (\frac{2}{5} ) [/tex]
The required probability that Gina wins is the sum of the above 3 probabilities . That is the probability that Gina wins the match is
[tex] (\frac{2}{5} )^2 +(\frac{2}{5} )^2(\frac{3}{5} ) +(\frac{2}{5} )^2 (\frac{3}{5} )=\frac{4}{25} +\frac{12}{125} +\frac{12}{125} =\frac{44}{125} [/tex]
