Random Thoughts 2012 (COMP 066) Jan-Michael Frahm Jared Heinly (Dense models starting from 3 million images on a single PC in a day)

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

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?

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? season 1961 was extended from 154 to 162 games , 704 opportunities

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. After students have had the opportunity to play the game several times, ask students to look at the tally chart and complete the columns by counting how many times each ladybug won. • Discuss these questions: Is the game fair? Does each ladybug have an equal chance to win? Would the results change if we played the game 5 more times? Explain.

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?