Random Thoughts 2012
(COMP 066)
Jan-Michael Frahm
Jared Heinly
Lessons from Reading Assignment
• The probability that two events will occur can never be
greater than the probability that each will occur
individually.
 “a good story is often less probable than a less satisfying …
[explanation]”
• Missing information
• Availability bias
 recallable prior knowledge influences our estimates
2
Game show problem
In a game show there are 3 doors behind one of the doors
there is a car and behind the other two doors there are goats.
During the game the participant selects one out of three
doors. Then the host will open one of the other doors that
has a goat behind it.
Then the participant can either switch to the other door or
stay with the door he has selected.
Is it better to switch or is it better not to switch?
3
Home Run Record
• 1961 historic race between Maris and Mantle for breaking
the homerun record of 60 of Babe Ruth’s
• Maris an underdog who never hit more than 39 homeruns
a year before and not after this year either (in 1960 he hit 1
homerun every 14.7 opportunities)
• Mantle was close to 50 homeruns a year (in 1960 he hit 1
homerun every 12.8 opportunities)
• Later people are talking about wrongdoing of Maris. Are
they right?
4
Dice Game
• Players choose their ladybug numbers and place ladybugs
on those numbers. If 2 players, each player gets 3 ladybugs
to place. If 3 players, each player gets 2 ladybugs to place.
• Player A tosses the die and the player whose ladybug has
that number of spots moves 1 space.
• Player B tosses the die and the player whose ladybug has
that number of spots moves 1 space.
• Play continues until the first ladybug reaches her home.
• The winning player makes a tally next to the winning
ladybug on the Class Recording Sheet.
5
Dice Game
Each player’s turn consists of repeatedly rolling a die. After
each roll, the player is faced with two choices: roll again, or
hold (decline to roll again).
 If the player rolls a 1, the player scores nothing and it
becomes the opponent’s turn.
 If the player rolls a number other than 1, the number is added
to the player’s turn total and the player’s turn continues.
 If the player holds, the turn total, the sum of the rolls during
the turn, is added to the player’s score, and it becomes the
opponent’s turn.
• What is a good strategy to win?
6