Name: _________________________________ Name: _______________ Date: _____________ Do Now In at least three sentences, describe what is going on in the situation below. _________________________ _________________________ _________________________ _________________________ _________________________ _________________________ __________________________________________________ __________________________________________________ The results of a survey of 80 households in Westville are shown below. 1. If Westville has 15,200 households, predict the number of households that will have exactly 3 computers? 2. How many households will have 2 or 3 computers?
Bourque/Laughton Probability– Day 1 EXPERIMENTAL VS. THEORETICAL PROBABILITY ACTIVITY __________________________________ is a value from 0 to 1 that measures the likelihood of an event. In this activity, you will investigate the difference between theoretical and experimental probability by tossing a coin. Coin Toss 1. When tossing a coin one time, there are only _____ possible outcomes. What are they? _____________________________________________________ a. P(heads) =________ b. P(tails) =_________ Theoretical Probability If you toss a coin 10 times, how many heads should you get? __________ Percent= How many tails should you get? ___________ Percent= Experimental Probability Toss your coin 10 times. Record the number of heads. _________ Percent= Toss your coin 10 times. Record the number of tails. _________ Percent= 2. Did you get the number of heads and the number of tails that you expected when you tossed the coins?_____________________
EXPERIMENTAL VS. THEORETICAL • _________________________________ probability of an event measures the likelihood that the event occurs based on actual results of an experiment. • Example 1: A quality control inspector samples 500 LCD monitors and finds defects in three of them. • What is the experimental probability that a monitor selected at random with have a defect? • If the company manufactures 15, 240 monitors in a month, how many are likely to have a defect based on the quality inspector’s results? • Practice 1: A park has 538 trees. You choose 40 at random and determine that 25 are maple trees. • What is the experimental probability that a tree chosen at random is a maple tree? • About how many trees in the park are likely to be maple trees? • _________________________________ probability describes the likelihood of an event based on mathematical reasoning. • Example 2: You are rolling two dice • numbered 1 to 6. What is the probability • that you roll numbers that add to 7? • Practice 2: What is the probability that • you roll a sum of 9?
PRACTICE • A baseball player got a hit 19 times of his last 64 times at bat. • What is the experimental probability that the player got a hit? • If the player comes up to bat 200 times in a season, about how many hits is he likely to get? • A medical study tests a new cough medicine on 4,250 people. It is effective for 3982 people. • What is the experimental probability that the medicine is effective? • For a group of 9000 people, predict the approximate number of people for whom the medicine will be effective? • A bag contains letter tiles that spell the name of the state MISSISSIPPI. Find the theoretical probability of drawing one tile at random for each of the following. • a. P(M) = b. P(I) = • c. P(S) = d. P(P) = • e. P(not M) = f. P(not I) = • g. P(not S) = h. P(not P) =
PROBABILITY DISTRIBUTIONS AND FREQUENCY TABLES • A _________________________________ _______________ is a data display that shows how often an item appears in a category. • The table at the below shows the speeds of cars as they pass a certain mile marker on highway 66. The speed limit is 65 mph. • a. What is the total number of • cars that pass the marker? • b. What is the probability that a car • stopped at random will be traveling • faster than the speed limit? • _______________________________ _________________________ is the ratio of the frequency of the category of the total frequency. • Example 3: The results of a survey of students’ music • preferences are organized in the frequency table to the • right. What is the relative frequency of preference for • rock music? • Practice 3: What is the relative frequency of the • following? • a. Classical • b. Hip Hop • c. Country
PRACTICE • A student conducts a probability experiment by tossing 3 coins one after the other. Using the results below, what is the probability that exactly three heads will occur in the next three tosses? • A student conducts a probability experiment by spinning a spinner divided into parts numbered 1 - 4. Using the results in the frequency table, what is the probability of the spinner pointing at 4 on the next spin? • In a recent competition, 50 archers shot 6 arrows each at a target. Three archers hit no bull’s eyes; 7 hit two bull’s eyes; 7 hit three bull’s eyes; 11 hit four bull’s eyes; 10 hit five bull’s eyes; and 7 hit six bull’s eyes. Fill in the table below. • The table below shows the number of text messages sent in one month by students at Metro High School. • a. If a student is chosen at random, what is the • probability that the student sends 1500 or • fewer text messages in one month? • b. If a student is chosen at random, what is the • probability that the student sends more than • 1500 messages a month?
Bourque/Laughton Homework 8-1 Name: _________________________________ Date: _______________ Period: _____________ • Homework 8-1: Probability • Suppose you flip a coin three times, what is the theoretical probability that you flip three heads? • A music collection includes 10 rock CDs, 8 country CDs, 5 classical CDs, and 7 hip hop CDs. • What is the probability that a CD randomly selected from the collection is a classical CD? • What is the probability that a CD randomly selected from the collection is not a classical CD? • You are playing a board game with a standard number cube (numbered 1 – 6). It is your last turn and if you roll a number greater than 2, you will win the game. What is the probability that you will not win the game? • If there is a 70% chance of snow this weekend, what is the probability that it will not snow? • From 15,000 graphing calculators produced by a manufacturer, an inspector selects a random sample of 450 calculators and finds 4 defective calculators. Estimate the total number of defective calculators out of 15,000. • A student randomly selected 65 vehicles in the student parking lot and noted the color of each. She found that 9 were black, 10 were blue, 13 were brown, 7 were green, 12 were red, and 14 were a variety of other colors. What is each experimental probability? • a. P(red) = b. P(not blue) = c. P(not green) =
The honor society at a local high school sponsors a blood drive. High school juniors and seniors who weigh over 110 pounds may donate. The table at the right indicates the frequency of donor blood type. • What is the relative frequency of blood type AB? • What is the relative frequency of blood type A? • Which blood type has the highest relative frequency? What is the relative frequency for this blood type? • The blood drive is extended for a second day, and the frequency doubles for each blood type. Do the relative frequencies change for each blood type? Explain. • Twenty-three preeschoolers were asked what there favorite snacks are. The results are show in the bar graph to the right. • What is the probability that a preschooler chosen at random chose popcorn as their favorite snack? • What is the probability that a preschooler chosen at random did not chose bananas as their favorite snack? • Complete the table below.