Unit 4 Sections 4-1 & 4-2

4-1 & 4-2: Sample Spaces and Probability  Probability – the chance of an event occurring.  Probability event – a chance process that leads to a well defined result (outcome).  Ex: rolling a die, flipping a coin  Outcome – the result of a single trial of a probability experiment.  Ex: flipping heads or tails  Sample Space – the set of all possible outcomes a probability experiment.

Determining Sample Spaces Section 4-2  Example 1 : Determine the sample space for each probability experiment. ExperimentSample Space Toss one coin Roll a die Answer a true/false question Toss Two Coins

Determining Sample Space Section 4-2  Example 2 : Determine the sample space for rolling two dice

Determining Sample Space Section 4-2  Example 3 : Determine the sample space for the gender of the children if a family has three children. (Use B for boy and G for girl)

Section 4-2  Tree Diagram – a device consisting of line segments emanating from a starting point and also from the outcome point.  Used to determine all possible outcomes of a probability experiment.  Example 4: Using a tree diagram, determine the sample space for the gender of the children if a family has three children.

 Event – set of outcomes of a probability event.  Ex: rolling and odd number  Event with one outcome is called a simple event.  Event with more than one outcome is called a compound event.  Classical probability – the use of sample spaces to determine the numerical probability that an event will happen.  Equally Likely Events – events that have the same probability of occurring.  Ex: flipping heads or tails. Section 4-2

Formula for Classical Probability The probability of any event E is: The number of outcomes in E Total number of outcomes in the sample space Section 4-2

 Example 5:  A) For a card drawn from an ordinary deck, find the probability of getting a queen.  B) If a family has three children, find the probability that all the children are girls Section 4-2

 Example 6: A card is drawn from an ordinary deck. Find these probabilities:  Of getting a jack  Of getting the 6 of clubs  Of getting a 3 or a diamond  Of getting a 3 or a 6 Section 4-2

 Probability Rules:  The probability of any event is a number between (and including) 0 and 1.  If an event cannot occur, then the probability is 0.  If an event is certain, then the probability is 1.  The sum of the probabilities of all the outcomes in the sample space is 1. Section 4-2

 Complement of an event – the set of the outcomes in a sample space that are not included in the outcomes of the event.  The complement of E is denoted :  Example 7: Find the complement of each event:  Rolling a die and getting a 4.  Selecting a month and getting a month that begins with J.  Selecting a day of the week and getting a weekday. Section 4-2

 Empirical probability – probability that relies on actual experience to determine the likelihood of outcomes.  also known as experimental probability Example 8: 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 person has type O blood  A person has type A or B blood  A person does not have type AB blood Section 4-2

 Subjective Probability – a probability value based on an educated guess or estimate, employing opinions and inexact information.  Ex: A doctor might say that there is a 30% chance that a patient will need surgery. Section 4-2

Homework:  Pg 186: 13, 15,