Question

PROBABILITY QUESTION

William Gates is about to play a three-game chess match with Steve Jobs, and wants to nd the strategy
that maximizes his winning chances. Each game ends with either a win by one of the players, or a draw.
If the score is tied at the end of the two games, the match goes into sudden-death mode, and the players
continue to play until the rst time one of them wins a game (and the match). William has two playing
styles, timid and bold, and he can choose one of the two at will in each game, no matter what style he chose
in previous games. With timid play, he draws with probability 0.65, and he loses with probability 0.35. With
bold play. he wins with probability 0.60, and he loses with probability 0.4. William will always play bold
during sudden death, but may switch style between other games.

Question 1.1 Find the probability that Gates wins the match if he plays bold in all rst three
games.
Question 1.2 Find the probability that Gates wins the match if he plays timid in all rst three
games.

Answer 1

1.1 Probability of Gates winning the match, if he plays bold in all the 1st 3 games = 0.6 x 0.4 x 0.6 + 0.4 x 0.6 x 0.6 + 0.6 x 0.6 = 0.144 + 0.144 + 0.36 = 0.648

1.2 With timid play, Gates can't win any game.

The possible case for Gates to win the match, given he plays timid in the first 3 games is Draw, Draw, Draw, Win (Bold style)

The probability = 0.65 x 0.65 x 0.65 x 0.6 = 0.1648