Presentation on theme: "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."— Presentation transcript:
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. 123456 1 2 3 4 5 6
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