Probability• Dice – coke bottle cap• Coin toss – games• Short run vs. long run behavior – Toss

coin 10 times

• 10 tosses vs. 500 tosses.

Probability• Law of Large Numbers – The more and more repetitions observed

of any chance process, the proportion of times that a specific outcome occurs approaches a single value

• This single value is called the probability of that specific outcome occurring

Probability• Probability is a value between 0 & 1 that

describes how often (the proportion of times) an outcome of a chance process occurs in a very long series of repetitions.

• An outcome that never occurs has a probability of 0

• An outcome that always occurs has a probability of 1

• An outcome that occurs half of the time in a very long series of trials has a probability of 0.5

Myths of Probability• Pg. 286 • Short-run regularity MYTH: random

phenomena is not predictable in the short-run

Which of the following outcomes of tossing a coin six times is more probable?

HTHTTH TTTHHH

Myths of Probability• Law of Averages MYTH: the idea that

future outcomes will make up for some imbalance, that the next rolls or tosses will balance things out

• Toss – if you get TTTTTT• Shots – hot hand• Babies – girls vs. boys

• Dice, coins, spinners have NO MEMORY!!

Myths of Probability• With your table mate record the results

for flipping a coin 30 times. Write your results in groups of 5 so it is easier to read. ex. HTHTT THHHT

• Count the number of runs of each outcome of size 2, 3, 4, and so on

• Calculators randint (1,2)

Run Length 2 3 4 5 6 7 Frequency