Bryce, a baseball player who tends to have "streaks", hit a home run during the first game of the season. The conditional probability that he will hit at least 1 home run in a game is 0.5 if he hit at least 1 home run in the previous game, but it is only 0.1 if he hit no home runs in the previous game. Bryce plays in all games during the season.
(a) What is the probability that Bryce will hit no home runs during the third game of the season?
(b) If we know that Bryce hit a home run during the ninth game, what is the probability that he will hit at least 1 home run during the tenth game?
(c) What is the probability that Bryce will hit at least 1 home run during the 150th game of the season?
(d) What is the probability that Bryce will both hit at least 1 home run during the 150th game of the season, and hit no home runs during the 151st game of the season?