Yusuf Sila: GAME THEORY PROBLEMS

GAME THEORY PROBLEMS

12:24 AM

Muhammad Yusuf , Posted in Logic , 0 Comments

If there are 2 apples, 1 orange, and 3 peaches in the basket and the same rules from the example apply, which type fruit will be left in the basket?
In the Stanley Cup playoffs, two teams play a maximum of 7 games against each other and the team that wins 4 games moves on to the next round. After a team has won its 4th game, no more games are played; for example, if the Leafs win 2 games, the Senators win 1 game, and the Leafs win 2 more games for a total of 5 games, then the Leafs will move on to the next round and the 6th and 7th games will not be played.

If the Leafs won the first two games against the Senators and the Sens won the third game, construct a game tree to find all of the possible outcomes of the rest of the round.
If each of the outcomes listed in part (a) are equally likely to occur, what is the probability that the Senators will win the round? (Hint: the probability that an event will occur is the number of ways that the event can occur divided by the total number of outcomes.)
What is the probability that the Leafs will win the round in six games or less?

Andrew and Bethany are playing a game where they take turns taking marbles out of three jars. Andrew goes first. For each turn, the player must take the same number of marbles out of any two jars (for example, if Bethany takes two marbles out of one jar, she must also take two marbles out of another jar). The person who cannot make any more moves loses (ie. the person who is left with two or more empty jars loses). The first jar has 1 marble in it, the second jar has 2 marbles and the third jar has 5 marbles. Draw a game tree to find all of the possible outcomes. If each of the outcomes you found has the same chance of occurring, then who is more likely to win?