Transcript Probability
9-1 Probability Warm Up Write each fraction in simplest form. 1. 16 20 4 5 2. 12 36 1 3 3. 8 64 1 8 4. 39 195 1 5 Pre-Algebra 9-1 Probability Learn to find the probability of an event by using the definition of probability. Pre-Algebra 9-1 Probability Vocabulary experiment trial outcome sample space event probability impossible certain Pre-Algebra 9-1 Probability An experiment is an activity in which results are observed. Each observation is called a trial, and each result is called an outcome. The sample space is the set of all possible outcomes of an experiment. Experiment Sample Space flipping a coin heads, tails rolling a number cube 1, 2, 3, 4, 5, 6 guessing the number of jelly beans in a jar whole numbers Pre-Algebra 9-1 Probability An event is any set of one or more outcomes. The probability of an event, written P(event), is a number from 0 (or 0%) to 1 (or 100%) that tells you how likely the event is to happen. • A probability of 0 means the event is impossible, or can never happen. • A probability of 1 means the event is certain, or has to happen. • The probabilities of all the outcomes in the sample space add up to 1. Pre-Algebra 9-1 Probability Never happens Happens about half the time Always happens 1 2 3 4 1 0 1 4 0.25 0.5 0.75 1 0% 25% 50% 75% 100% 0 Pre-Algebra 9-1 Probability Example 1A: Finding Probabilities of Outcomes in a Sample Space Give the probability for each outcome. A. The basketball team has a 70% chance of winning. The probability of winning is P(win) = 70% = 0.7. The probabilities must add to 1, so the probability of not winning is P(lose) = 1 – 0.7 = 0.3, or 30%. Pre-Algebra 9-1 Probability Example 1B: Finding Probabilities of Outcomes in a Sample Space Give the probability for each outcome. B. Three of the eight sections of the spinner are labeled 1, so a reasonable estimate of the probability that the spinner will land on 1 is 3 P(1) = . 8 Pre-Algebra 9-1 Probability Example 1B Continued Three of the eight sections of the spinner are labeled 2, so a reasonable estimate of the probability that the spinner will land on 2 is P(2) = 3 . 8 Two of the eight sections of the spinner are labeled 3, so a reasonable estimate of the probability that the spinner will land on 3 is P(3) = 2 = 1 . 8 4 Check The probabilities of all the outcomes must add to 1. 3 3 2 + + = 1 8 8 8 Pre-Algebra 9-1 Probability Example 2A Give the probability for each outcome. A. The polo team has a 50% chance of winning. The probability of winning is P(win) = 50% = 0.5. The probabilities must add to 1, so the probability of not winning is P(lose) = 1 – 0.5 = 0.5, or 50%. Pre-Algebra 9-1 Probability Example 2B Give the probability for each outcome. B. Rolling a number cube. Outcome 1 2 3 4 5 Probability One of the six sides of a cube is labeled 1, so a reasonable estimate of the probability that the spinner will land on 1 is P(1) = 1 . 6 One of the six sides of a cube is labeled 2, so a reasonable estimate of the probability that the spinner will land on 2 is P(2) = 1 . 6 Pre-Algebra 6 9-1 Probability Example 2B Continued One of the six sides of a cube is labeled 3, so a reasonable estimate of the probability that the spinner will land on 3 is P(3) = 1 . 6 One of the six sides of a cube is labeled 4, so a reasonable estimate of the probability that the spinner will land on 4 is P(4) = 1 . 6 One of the six sides of a cube is labeled 5, so a reasonable estimate of the probability that the spinner will land on 5 is P(5) = 1 . 6 Pre-Algebra 9-1 Probability Example 2B Continued One of the six sides of a cube is labeled 6, so a reasonable estimate of the probability that the spinner will land on 6 is P(6) = 1 . 6 Check The probabilities of all the outcomes must add to 1. 1 1 1 1 1 1 + + + + + =1 6 6 6 6 6 6 Pre-Algebra 9-1 Probability To find the probability of an event, add the probabilities of all the outcomes included in the event. Pre-Algebra