Probability results

Experiment #1a: Tossing One Die Toss one die 30 times, record TOSSING 1 DIEP(1)P(3)P(5) P(even number) Sample Empirical ResultsUse P(E)= n(E) / total tosses 5/30 =.176/30 =.24/30 =.1315/30 =.5 Your Empirical Results Class Empirical Results Theoretical Results Use P(E)= n(E) / n(S) where S=SampleSpace 1/6 =.167 3/6 = 1/2

Law of large numbers Last 2 rows (experimental and theoretical) should be similar

Experiment #1b: Tossing Two Dice Consider the following game: When tossing two dice, anyone on Team A wins a point each time the sum of the dice comes up as a 6, 7, 8, or 9. Anyone on Team B wins anytime a sum different from 6,7,8, or 9 appears. Which team would you think had a better chance of winning -- Team A or Team B? Try the experiment by tossing the pair of dice 20 times and recording your results. Record the empirical probability that:

Expt 1b TOSSING 2 DICEP(Team A- 6, 7, 8, 9)P(Team B-all others) Which do you think will win and why? Sample Empirical Results Use P(E)= n(E) / total tosses 12/20 =.68/20 =.4 Your Empirical Results Class Empirical Results Theoretical ResultsUse P(E)= n(E) / n(S)

Experiment #1c: Tossing One Coin When flipping a coin, how likely is a head? Try 10 times. TOSSING 1 COINP(head) how often do you expect to toss a head? Sample Empirical Results Use P(E)= n(E) / total tosses 6/10 = 0.6 Your Empirical Results Class Empirical Results Theoretical ResultsUse P(E)= n(E) / n(S)

Experiment #1d: Tossing Two coins If flipping 2, predict. Do 20 times TOSSING 2 COINSP(2 heads, 0 tails)P(1 head, 1 tail)P(0 heads, 2 tails) Guess: how often would you expect each possibility? Sample Empirical Results Use P(E)= n(E) / total tosses 8/30 =.2714/30 =.478/30 =.27 Your Empirical Results Class Empirical Results Theoretical Results Use P(E)= n(E) / n(S)

Experiment #1e: Tossing Three Coins: Do 20 times TOSSING 3 COINS P(3 heads) P(2 heads)P(1 head)P(0 heads) Guess: how often would you expect each? Sample Empirical Results Use P(E)= n(E) / total tosses 3/20=.15 7/20 =.356/20 =.34/20 =.2 Your Empirical Results Class Empirical Results Theoretical Results Use P(E)= n(E) / n(S)