Review Homework pages Example: Counting the number of heads in 10 coin tosses. 2.2/ both odd ¼ 5. 61/ yellow, 2 red, 4 blue,5 green

Bus Plane Bus Plane Car Plane Bus Plane Car Bus Plane Bus Bus Car Car Plane Car Bus Car Page 117 #5 - 7 #6 12 #7 ½ #5

More Probability

Sample Space and Events Sample space( 표본 공간 ) : The collection of all possible outcomes for an experiment. Event: A collection of outcomes for the experiment, that is, any subset of the sample space.

Probability Notation If E is an event, then P(E) stands for the probability that event E occurs. It is read “the probability of E”

Venn diagram for event E

Relationships Among Events (not E): The event that “E does not occur.” (A & B): The event that “both A and B occur.” (A or B): The event that “either A or B or both occur.”

The Classic Deck of 52 Playing Cards 4 Suits: Spades ♠, Hearts ♥, Clubs ♣, Diamonds ♦ Each suit is made up of 13 cards or ranks. A (ace), 2, 3, 4, 5, 6, 7, 8, 9, 10, J (jack), Q (queen), K (king). Ace is usually considered high. J, Q, K are the face cards

A Deck of Cards Hearts ClubsDiamonds Spades

Sample space for rolling a die once

Event (not E) where E is the probability of drawing a face card. 40/52=10/13

Sample Space-1 Red Die, 1 Green Die - 36 Total Outcomes Sample Space-Red Die, Green Die

The Sum of Two Die Tosses What is the probability that the sum will be 5? 7? What is the probability that the sum will be 10 or more? What is the probability that the sum will be either 3 or less or 11 or more? 4/36=1/9 6/36=1/6 3/36 + 3/36=1/6

Probabilities of 2 throws of the die What is the probability of a 1 and a 3? What is the probability of two sixes? What is the probability of at least one 3? 2/36 1/36 11/36

Dice Roll by computer ExpProbability/

Two computer simulations of tossing a fair coin 100 times

Law of Large Numbers The greater the number of trials the more likely the experimental probability of an event will equal its theoretical probability.

Tossing coins flip-probability-simulator/

Counting Principle If there are m ways to do one thing, and n ways to do another, then there are m * n ways of doing both.

Basic Properties of Probabilities Property 1: The probability of an event is always between 0 and 1, inclusive. Property 2: The probability of an event that cannot occur is 0. (An event that cannot occur is called an impossible event.) Property 3: The probability of an event that must occur is 1. (An event that must occur is called a certain event.)

A Deck of Cards Hearts ClubsDiamonds Spades

The event the king of hearts is selected 1/52

The event a king is selected 1/13 = 4/52

The event a heart is selected 1/4 = 13/52

What is the probability of an event that a face card is selected 3/13=12/52

An event and its complement

Homework Tree Diagram Worksheet