When Stephane plays chess against his favorite computer prog

When Stephane plays chess against his favorite computer program he wins with probability 0.60 loses with probability 0.10 and 30% of the games result in a draw. Assume independence.

a) Find the probability that Stephane\'s first win happens when he plays his third game.

b) Find the probability that Stephane\'s fifth win happens when he plays his eighth game.

c) Find the probability that Stephane wins 7 games if he plays 10 games.

Stephane plays 12 games.

d) Find the probability that he wins 5 games, loses 3 games, and draws 4 games.

e) Find the probability that he wins 7 games, and draws 5 games.

f) Find the probability that Stephane wins at least 8 games.

Solution

a) Find the probability that Stephane\'s first win happens when he plays his third game

= he loses first two and wins iii

= (0.4)²(0.6)

b) the probability that Stephane\'s fifth win happens when he plays his eighth game =

prob he wins 4 times in 7 games and he wins 8th game

= 7C4(0.6)⁴(0.4)³(0.6)

c)

probability that Stephane wins 7 games if he plays 10 games.

= 10C7(0.6)⁷(0.4)³

d) the probability that he wins 5 games, loses 3 games, and draws 4 games.= 12C5(0.6)⁴7c3(0.1)³(0.3)⁴

^e) the probability that he wins 7 games, and draws 5 games

= 12C5(0.6)⁷(0.3)⁵

^f) the probability that Stephane wins at least 8 games.=P(X>=8 in binomial with p = 0.6)

= 12C8(0.6)⁸(0.4)⁴