How do we use empirical probability?

HW#3: Chapter 4.2 page 255 #4.22 and 4.24

Four Basic Probability Rules

1. The probability of any event E is a number (either a fraction or a decimal) between and including 0 and 1. This is denoted by

2. If an event E cannot occur, it is a probability of 03. If an event E is certain, then the probability of E

is 14. The sum of the probability of all the outcomes in

the sample space is 1

0 ( ) 1P E

What is a complement of an event?

• The complement of an event E is the et of outcomes in the sample space that are not included in the outcomes of event E. The complement of E is denoted by

• Example: Find the complement of each event1. Rolling a die and getting a 4. (Ans: Getting a 1, 2,

3, 5, 6)2. Selecting a letter of the alphabet and getting a

vowel. (Ans: Getting a consonant – assuming y is a constant)

E

The Rule for Complementary Events

( ) 1 ( )

( ) ( ) 1

P E P E

P E P E

Example: If the probability that a person lives in an industrialized country of the world is 1/5, find the probability that a person does not live in an industrialized country.

Ans: P(not living in an industrialized country) = 1 – P(living in industrialized country) = 1 – 1/5 = 4/5

What is Empirical Probability?

• Empirical Probability: relies on actual experience to determine the likelihood of outcomes – Example: You may actually roll the die 600 times

to observe the various frequencies

Formula for Empirical Probability

• Given a frequency distribution, the probability of an event being in a given class is

P(E) = frequency for the class = ftotal frequency in the distribution n

• This probability is called empirical probability and is based on observation.

Example Empirical Probability

• In the soft drink survey, find the probability that a person responded no

response frequencyYes 15No 8Undecided 2

Ans: P(E) = f/n = 8/25

“And” / “Or”

• In probability:– And = subtract– Or = Add

“At Least” / “At Most”

• At Least: that number and higher to the max– P(at least rolling a 4) = P(4) or P(5) or P(6)– P(at least rolling a 4) = P(4) + P(5) + P(6)

• At Most: that number down to zero/minimum outcome– P(at most rolling a 2) = P(2) or P(1)– P(at most rolling a 2) = P(2) + P(1)

Class Work1. Find the complement of (a) Selecting a month and getting a month that begins with a J; (b)

selecting a day of the week and getting a weekday.2. How is empirical probability difference from classical probability?3. In a sample of 50 people, 21 had type O blood, 22 had type A blood, 5 had type B blood, and 2

had type AB blood. Set up a frequency distribution and find the following probabilities:a. A person has type O bloodb. A person has type A or type B bloodc. A person has neither type A nor type O bloodd. A person does not have type AB blood

4. Hospital records indicated that maternity patients stayed in the hospital for the number of days shown in the distribution. Number of Days Stayed

Frequency3 154 325 566 197 5

Find the probability of: a. a patient staying exactly 5 daysb. a patient staying less than 6 daysc. a patient staying at most 4 daysd. a patient staying at least 5 days