Day 2 Tuesday! Warm-Up… Quickwrite… (If you did not do the Homework) Write your own example for each of the different probability assignments Intuition Relative Frequency Formula Quickwrite… If you could change the color of your eyes, what would you change them to? Why? Ex: “If I could change the color of my eyes, I would change them to __________ because ______________________.”

Compare and Explain… your Warm-Up starting with Student #2 (1 min) Write your own example for each of the different probability assignments Intuition Relative Frequency Formula

Round Robin… starting with the student with the driest clothes at your table (1 min) If you could change the color of your eyes, what would you change them to? Why? Ex: “If I could change the color of my eyes, I would change them to __________ because ______________________.”

Basic rules of Probability

Law of Large Numbers The underlying assumption we make is that if events occurred a certain percentage of times in the past, they will occur about the same percentage of times in the future The law of large numbers is the reason businesses such as health insurance, automobile insurance, and gambling casinos can exist and make a profit To determine the possible outcomes for a given setting, we need to define a statistical experiment

What is a Statistical Experiment?

Example: Eye Color

Example: Eye Color Human eye color is controlled by a single pair of genes (one from the father and one from the mother) called a genotype Brown eye color, B, is dominant over blue eye color, Therefore, in the genotype B , consisting of one brown gene B and one blue gene , the brown gene dominates A person with a B genotype has brown eyes.

Example: Eye Color If both parents have brown eyes and have genotype B , what is the probability that their child will have blue eyes? What is the probability the child will have brown eyes? According to genetics theory, the four possible genotypes for the child are equally likely Eye Color Genotypes for Child

Example: Eye Color Therefore, we can use the Formula for Equally Likely Outcomes to compute probabilities Blue eyes can occur only with the genotype, so there is only one outcome favorable to blue eyes Brown eyes occur with the three remaining genotypes: BB, B , and B

Practice

The Sum of Probabilities We can use this fact to determine the probability that an event will not occur For instance, if we think the probability is 0.65 that we will win a tennis match, we assume the probability is 0.35 that the opponent will win The complement of an event A is the event that A does NOT occur: we use the notation Ac

Event A and Its Complement Ac

Example: Complement of an Event The probability that a college student who has not received a flu shot will get the flu is 0.45 What is the probability that a college student will not get the flu if the student has not had the flu shot? In this case, we have P (will get flu) = 0.45 P (will not get flu) = 1 – P (will get flu) = 1 – 0.45 = 0.55

Practice

Probability Related to Statistics

Homework