Welcome! U4H2: Worksheet # s 2-7, 9-13, 16, 20 Updates: U4T is 12/12 Announcement: December 16 th is the last day I will accept late work.
1 Review U4H1 2 Theoretical Probability 3 Experimental Probability 4 Cool-Down! Agenda
Review U4H1
Warm-Up! (1) Compare. Write >, <, or =. (a) 7 P 4 7 P 3 (b) 7 P 3 7 C 4
Warm-Up! (2) How many ways can you choose a manager and assistant from a 9-person task force? 72 (3) There are 5 airplanes ready to depart. Runway A and runway D are available. How many ways can 2 planes be assigned to runways without using the same runway? 20
Setting up your Notebook Leave one page blank for supplemental notes. Today s Lesson #: ---- Topic: Theoretical vs. Experimental Probability LO#2: Determine the theoretical or experimental probability of an event.
Probability Probability The measure of how likely an event is to occur. Each possible result of a probability experiment or situation is an outcome. The set of all possible outcomes is the sample space. An event is an outcome or set of outcomes.
Probability Probability Written as a fraction or decimal from 0 to 1, or as percent's from 0% to 100%.
Types of Outcomes Equally likely outcomes Probability Have the same chance of occurring. Example: You toss a fair coin, heads and tails are equally likely outcomes. Favorable outcomes Outcomes in a speciwied event. Example: You toss a fair coin, what is the probability of landing on a tails? The favorable outcomes for a tails is 1.
Theoretical Probability Theoretical Probability It is the likeliness of an event happening based on all the possible outcomes. An event is the ratio of the number of favorable outcomes to the total number of outcomes.
Practice: Theoretical Probability (1) Each letter of the word PROBABLE is written on a separate card. The cards are placed face down and mixed up. What is the probability that a randomly selected card has a consonant? (2) Two number cubes are rolled. What is the probability that the difference between the two numbers is 4? (3) A red number cube and a blue number cube are rolled. If all numbers are equally likely, what is the probability of the event? The difference is 6.
Theoretical Probability
Practice: Theoretical Probability (4) A gumball machine contains 20 yellow gumballs, 12 green gumballs, and 13 pink gumballs. What is the probability that the next gumball that comes out will be either yellow or green? (5) You pick one card from a standard deck. What is the probability that the card will not be a red card? (6) A jar contains 3 blue, 6 green, and 2 red marbles. If you pick one without looking, what is the probability that the marble you pick will be neither blue nor green?
Complement Theoretical Probability The complement of an event E is the set of all outcomes in the sample space that are not in E.
Practice: Theoretical Probability (7) There are 25 students in study hall. The table shows the number of students who are studying a foreign language. What is the probability that a randomly selected student is not studying a foreign language? Language Number French 6 Spanish 12 Japanese 3 (8) Two integers from 1 to 10 are randomly selected. The same number may be chosen twice. What is the probability that both numbers are less than 9?
Practice: Theoretical Probability (9) Each student receives a 5-digit locker combination. What is the probability of receiving a combination with all odd digits?
Theoretical Probability Geometric Probability A form of theoretical probability. P(a point chosen at random in ) = the area or volume that you want divided by the area or volume of the entire Wigure.
Practice: Theoretical Probability (10) A Wigure is created placing a rectangle inside a triangle inside a square as shown. If a point inside the Wigure is chosen at random, what is the probability that the point is inside the shaded region? (11) Find the probability that a point chosen at random inside the large triangle is in the small triangle.
Experimental Probability Experiential Probability Is often used to estimate theoretical probability and to make predictions. Each repetition of an experiment is a trial. Example: Sam rolled a number cube 50 times. A 3 appeared 10 times. Then the experimental probability of rolling a 3 is 10 out of 50 or 20%.
Practice: Experimental Probability (12) The table shows the results of a spinner experiment. Find the experimental probability of spinning a 4. Number Occurrences 1 6 2 11 3 19 4 14 (13) The table shows the results of choosing one card from a deck of cards, recording the suit, and then replacing the card. Find the experimental probability of choosing a diamond.
Experimental Probability Practice: Identify the type of probability being used (theoretical, complement, geometric, or experimental). Answer the question. (14) In a box of 25 switches, 3 are defective. What is the probability of randomly selecting a switch that is not defective? (15) There are 12 E s among the 100 tiles in Scrabble. What is the probability of selecting all 4 E s when selecting 4 tiles?
Experimental Probability (16) The table shows the results of rolling a die with unequal faces. Find the experimental probability of rolling 1 or 6. (17) A fruit bowl contains 4 green apples and 7 red apples. What is the probability that a randomly selected apple will be green?
Experimental Probability (18) Joanne is guessing which day in November is Bess s birthday. Joanne knows that Bess s birthday does not fall on an odd-numbered day. What is the probability that Joanne will guess the correct day on her Wirst try? (19) Tom has a dollar s worth of dimes and a dollar s worth of nickels in his pocket. a. What is the probability he will randomly select a nickel from his pocket? b. What is the probability he will randomly select a dime from his pocket?
Cool-Down! On your whiteboard we will do the following practice: h)p://my.hrw.com/math06_07/nsmedia/prac>ce_quizzes/ alg2/alg2_pq_prs_02.html