Clair and Helen frequently play each other in a series of games of table tennis. Records of the outcomes of these games show that whenever they play a series of games, Clair has a probability 0.6 of winning the first game and that in every subsequent game in the series, Clair's probability of winning the game is 0.7, if he won the preceeding game but only 0.5 if he lost the preceeding game.
A table tennis game cannot be drawn.
Find the probability that Clair will win the third game in the next series of games palyed against Helen.