# This is your presentation title Probability Carnival Hello! Kathy Allen [email protected] 2 New Teams Icebreaker: 3 minutes. Send an email introducing yourselves and asking a QR

question. 3 Team goal WIN!!! 4 Lets Play Dice! One player rolls One player records One player keeps a tally

Probabilit y All probabilities must be between 0 1. All probabilities add to equal 1. 6 Probability Experimental

Theoretical After 210 rolls After 1500 rolls 300 35 30 250

25 200 20 150 15 100

10 50 5 0 0 2 3 4

5 6 7 8 9 10

11 12 2 3 4 5

6 7 8 9 10 11

12 7 Combined Probability For two independent events A, B: Probability of events A AND B =P(A) * P(B) AND means MULTIPLY 8

Whats the probability of rolling a sum of two, then a sum of three? P(Sum of two) AND P(Sum of three) 9

Choose a game, Fix your probabilities Reminder: Money available only in \$5 and \$10 denominations Expected Value = (probability of event 1)*(value of event 1) + (probability of event 2)*(value of event 2) + (probability of event 3)*(value of event 3). An average you can expect to win/lose as you play a game repetitively

11 Expected Value Example Youre playing roulette at a casino. You bet \$5 on red. If you win, you win \$10 (net profit of \$5). If you lose, youre out \$5. Whats the expected outcome? EV=(Probability of Win)*(profit) + (Probability of Loss)*(\$ lost) EV = EV = -\$0.26 12

How do we make sure we win? Expected Value = (prob.1)*(value1) + (prob.2)*(value2) + . 13 Design a profitable game Reminder: Money available only in \$5 and \$10 denominations Make a poster advertising your

game Evaluate Others 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? 15

PLAY BALL!!- 25 min Reminders: You may not play your own game You must play every game once You must spend all player money 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 17 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? Lets review some concepts Probability Expected Value = (prob.1)*(value1) + (prob.2)*(value2) + (prob3)*(event3)+ .

19 Thanks! Slides available in Symbaloo Any questions? You can find me at [email protected] 20