Transcript Lesson 33
Bell Quiz Objectives • Identify whether events are independent or dependent. • Apply the rules of probability to determine the probability of an event. Independent Events • Events where the outcome of one does not affect the probability of the other are called independent events. • To find the probability of two independent events, multiply the probabilities of the two events. Example • Spinning a spinner and flipping a coin are independent events. • The results of one does not affect the result of the other. • What is the probability of spinning a 5 and landing on heads? Example • Spinning the spinner twice also creates two independent events. • The first spin does not affect the second spin. • What is the probability of spinning a 5 and then a 1? Dependent Events • With dependent events, the outcome of one event does affect the probability of the other event. • To find the probability of two dependent events, you multiply the probability of the first event by the probability of the second event, given the results of the first event. Independent and Dependent Events Example 1 Identifying Situations Involving Independent and Dependent Events Identify each set of events as independent or dependent. Rolling a 6 on one number cube and a 4 on another number cube. Example 2 Identifying Situations Involving Independent and Dependent Events Identify each set of events as independent or dependent. Rolling a 6 on a number cube and then a 4 on the same number cube. Example 3 Identifying Situations Involving Independent and Dependent Events Identify each set of events as independent or dependent. Drawing a red marble form a bag, keeping it out of the bag, and then drawing a blue marble. Example 4 Identifying Situations Involving Independent and Dependent Events Identify each set of events as independent or dependent. Drawing a red marble from a bag, putting it back in the bag, and then drawing a blue marble. Lesson Practice Identify each set of events as independent or dependent. A card is chosen from a deck of cards, replaced, and then a second card is chosen. Lesson Practice Identify each set of events as independent or dependent. A marble is drawn from a bag, kept, and then a second marble is drawn Lesson Practice Identify each set of events as independent or dependent. A coin is flipped, and a number cube is rolled. Lesson Practice Identify each set of events as independent or dependent. A spinner is spun and the result is recorded. Then the spinner is spun a second time. Example 5 Using a Tree Diagram • A tree diagram can help demonstrate the sample space for events. A coin is flipped twice. Make a tree diagram showing all possible outcomes. What is the probability of the coin landing on heads both times? Lesson Practice A coin is flipped and a six-sided number cube is tossed. Make a tree diagram showing all possible outcomes what is the probability of landing on tails and on an even number? Example 6 Calculating the Probability of Dependent Events Natalia has two squares and three circles in a bag. With out the use of a tree diagram, find the probability of drawing a circle, keeping it, and then drawing another circle. Lesson Practice A bag contains 4 red blocks and 3 blue blocks. Find the probability of drawing a red block keeping it, and then drawing another red block. Example 7 Calculating the Probability of Dependent Events Natalia has two squares and three circles in a bag. Find the probability of drawing a square, keeping it, and then drawing a circle. Lesson Practice A bag contains 4 red blocks and 3 blue blocks. Find the probability of drawing a blue block keeping it, and then drawing a red block. Odds • Odds are another way of describing the likelihood of an event. Odds are expressed as a ratio, usually written with a colon. Odds can be calculated for something or against something happening. Example 8 Calculating Odds A bag contains 6 red marbles, 2 yellow marbles, and 1 blue marble. What are the odds of drawing a red marble? Lesson Practice Use the spinner to answer the problem. What are the odds of spinning black? Example 9 Calculating Odds A bag contains 6 red marbles, 2 yellow marbles, and 1 blue marble. What are the odds against drawing a blue marble? Lesson Practice Use the spinner to answer the problem. What are the odds against spinning gray? Example 10 Solving Multi-Step Problems Involving Probability Isaac has 6 blue and 4 white shirts in his closet. There are also 2 pairs of navy pants and 3 pairs of khaki pants in his closet. What is the probability Isaac will choose khaki pants and a white shirt from his closet. Lesson Practice Campers select one inside activity and one outside activity daily. There are 5 inside activities and 8 outdoor activities. What is the probability of choosing pottery and horseback riding on the first day. Example 11 Solving Multi-Step Problems Involving Probability Isaac has 6 blue and 4 white shirts in his closet. There are also 2 pairs of navy pants and 3 pairs of khaki pants in his closet. The probability Isaac will choose khaki pants and a white shirt from 6 his closet is . Assume that after the pants and shirts are worn, 25 they are put in the laundry hamper. What is the probability that he will choose khaki pants and a white shirt from the closet to were the next day? Lesson Practice Campers select one inside activity and one outside activity daily. There are 5 inside activities and 8 outdoor activities. Inside activities can be repeated, but outside activities cannot be repeated. What is the probability of choosing pottery and swimming the second day?