LOGIC EXERCISE
8:46 PM
Muhammad Yusuf
, Posted in
1. 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?
2. 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.
(a) 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.
(b) 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.)
(c) What
is the probability that the Leafs will win the round in six games or less?
3. 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?
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