When Stephane plays chess against his favorite computer program he wins with the probability 0.60 loses with probability 0.10 and 30% of games result in a draw. Assume independence.
a) Determine the probability that Stephane's first win happens when he plays his third game.
b) Determine the probability that Stephane's fifth win happens when he plays his eighth game.
c) Determine the probability that Stephane wins 7 games if he plays 10 games.
Stephane plays 12 games.
d) Determine the probability that he wins 5 games, loses 3 games, and draws 4 games.
e) Determine the probability that he wins 7 games, and draws 5 games.
f) Determine the probability that Stephane wins at least 8 games.