Probability Carnival NEW TEAMS!!!

Kathy Allen kallen1@usi.edu Hello! Kathy Allen kallen1@usi.edu Introduce self; entry doc

New Teams Icebreaker: 3 minutes. Send an email introducing yourselves and asking a QR question.

Team goal – WIN!!!

Let’s Play Dice! One player rolls One player records One player keeps a tally Dice handout

Probability Number of desired results Total number of outcomes All probabilities must be between 0 – 1. All probabilities add to equal 1. Checkout 2-dice image, probability of rolling 7

Probability Experimental Theoretical

Combined Probability For two independent events A, B: Probability of events A AND B =P(A) * P(B) AND means MULTIPLY

What’s the probability of rolling a sum of two, then a sum of three? P(Sum of two) AND P(Sum of three) 1 36 ∗ 2 36 = 2 1296 = 1 648 =0.15%

Choose a game, Fix your probabilities Reminder: Money available only in $5 and $10 denominations 15:00 SHARP, use eggtimer

Expected Value = (probability of event 1)*(value of event 1) + An average you can expect to win/lose as you play a game repetitively Checkout 2-dice image, probability of rolling 7

Expected Value Example You’re playing roulette at a casino. You bet $5 on red. If you win, you win $10 (net profit of $5). If you lose, you’re out $5. What’s the expected outcome? EV=(Probability of Win)*(profit) + (Probability of Loss)*($ lost) EV = 18 38 ∗ $5 + 20 38 ∗ −$5 EV = -$0.26

How do we make sure we win? Expected Value = (prob.1)*(value1) + (prob.2)*(value2) + ………….

Design a profitable game Make a poster advertising your game Reminder: Money available only in $5 and $10 denominations Design a profitable game Make a poster advertising your game 15:00 SHARP, use eggtimer

Evaluate Other’s Games One player stays to explain game Others compute EV Whose game offers the lowest expected value? Whose game offers the highest expected value? Which games will you play?

PLAY BALL!!- 25 min Reminders: You may not play your own game You must play every game once You must spend all player money 15:00 SHARP, use eggtimer

Tally Results 1. Carnie money earned (grey)   2. Carnie prize money left (green) 3. Player 1 prize money 4. Player 2 prize money 5. Player 3 prize money Subtotal: add up lines 1-5 Penalty: subtract 2x leftover player grey money Subtract starting team amount: $350 carnie prize money, $140 per player Net earning ALSO SHARE EV of games

What Happened? Did play happen the way you expected? What did we learn? What are the advantages and disadvantages of learning this topic in this manner? 15:00 SHARP, use eggtimer

Let’s review some concepts Probability Number of desired results Total number of outcomes Expected Value = (prob.1)*(value1) + (prob.2)*(value2) + (prob3)*(event3)+ ………….

Thanks! Slides available in Symbaloo Any questions? You can find me at kallen1@usi.edu