Alec and Bill frequently play each other in a series of games of table tennis. Records of the outcomes of these games indicate that whenever they play a series of games, Alec has the probability 0.6 of winning the first game and that in every subsequent game in the series, Alec's probability of winning the game is 0.7 if he won the preceding game but only 0.5 if he lost the preceding game. A game cannot be drawn. Find the probability that Alec will win the third game in the next series he plays with Bill. (NEAB)