Name Date Class. Probability of Independent and Dependent Events

Transcription

1 -6 Practice Probability of In and Dependent Events Decide if each set of events is in or. Explain your answer. The first one has been started for you.. student spins a spinner and rolls a number cube. In 2. student picks a raffle ticket from a box and then picks a second raffle ticket without replacing the first raffle ticket. Find the probability of each set of in events. Choose the letter for the best answer. 3. drawing a black checker from a bag of 6 black checkers and 4 red checkers, replacing it, and drawing another black checker C flipping a tail on a coin and spinning a 5 on a spinner with sections of equal area numbered 5 C Solve rolling a six on the first roll of a 6 number cube and rolling an odd number on the second roll of the same cube C drawing a, 2, or 3 from 9 cards numbered 9, replacing the card, and drawing a 7, 8, or 9 7. There are 4 black marbles and 2 white marbles in a bag. What is the probability of choosing a black marble, not replacing it, then choosing a white marble? C Original content Copyright by Holt McDougal. dditions and changes to the original content are the responsibility of the instructor. 243 Holt McDougal Mathematics

2 -6 Practice Probability of In and Dependent Events Decide whether each set of events is in or. Explain your answer.. student spins a spinner and chooses a Scrabble tile 2. boy chooses a sock from a drawer of socks, then chooses a second sock without replacing the first. 3. student picks a raffle ticket from a box, replaces the ticket, then picks a second raffle ticket. Find the probability of each set of in events. 4. picking a red checker from a bag of 9 black checkers and 6 red checkers, replacing it, and picking another red checker 5. picking a black checker from a bag of 9 black checkers and 6 red checkers, replacing it, and picking a red checker 6. rolling a, 2, or 3 on the first roll of a 6 number cube and rolling a 4, 5, or 6 on the second roll of the same cube Solve. 7. Randy has 4 pennies, 2 nickels, and 3 dimes in his pocket. If he randomly chooses 2 coins, what is the probability that both are dimes? Original content Copyright by Holt McDougal. dditions and changes to the original content are the responsibility of the instructor. 245 Holt McDougal Mathematics

3 -6 Practice C Probability of In and Dependent Events Decide whether each set of events is in or. Explain your answer.. student spins an even number on a spinner and then spins another even number on the second spin. 2. student guesses on two multiple choice questions. Find the probability of each set of in events. 3. choosing a brown sock from a drawer of 4 brown socks, 0 black socks, and 6 gray socks, replacing it, then choosing a gray sock 4. choosing a pair of black socks from a drawer of 4 brown socks, 0 black socks, and 6 gray socks Solve. 5. Calista has 4 one-dollar bills, 2 five-dollar bills, and 3 ten-dollar bills in her wallet. If she randomly chooses 2 bills from her wallet, what is the probability that both are five dollar bills? 6. There are 0 true/false questions on a test. You do not know the answer to 4 of the questions, so you guess. What is the probability that you will get all 4 answers right? 7. There are 2 students in the fter-school Club. Three names are being selected at random to help with the school carnival. What is the probability that Jess, Sandy, and Phil will be chosen? Original content Copyright by Holt McDougal. dditions and changes to the original content are the responsibility of the instructor. 246 Holt McDougal Mathematics

4 -6 Problem Solving Probability of In and Dependent Events Write the correct answer.. Li rolls a pair of number cubes twice. On both rolls, the sum is 7. re the rolls or in events? Solution: The outcome of the first roll does not affect the outcome of the second roll. The events are in. 2. Nine boys and 2 girls want to play soccer. Teams are formed by selecting one player at a time. Is the probability of selecting a boy after a girl is selected a or an in event? How many people want to play soccer before the first player is picked? What is the probability of picking a boy first? What is the probability of picking a girl, once a boy has been picked? re the probabilities the same? The events are. Choose the letter for the best answer. 3. There are 8 blue marbles and 7 red marbles in a bag. Julie pulls two marbles at random from the bag first. What is the probability that she first pulls a blue marble and then a red marble? ndrew has $2.00 in quarters in his pocket, including three state quarters. He takes two quarters out of his pocket. What is the probability that they are not state quarters? You roll a 6 number cube twice. What is the probability that you roll a 3 on the first roll and a 6 on the second roll? Jamie has 3 raffle tickets. One hundred tickets were sold. Her name was not drawn for the first prize. What is the probability that her name will be drawn for the second prize? Original content Copyright by Holt McDougal. dditions and changes to the original content are the responsibility of the instructor. 247 Holt McDougal Mathematics

5 -6 Review for Mastery Probability of In and Dependent Events Events are in when the outcome of one event has no effect on the outcome of a second event. Rolling a number cube and flipping a coin are in events. Find the probability of rolling a 4 and flipping heads.. There are outcomes for the number cube and outcomes for the coin. 2. Using the Fundamental Counting Principle, there are, or, possible outcomes of rolling a number cube and flipping a coin. 3. Make a list of the possible outcomes: How many possible ways are there of rolling a 4 and flipping heads? 4. P(4 and heads) = number of ways 4 and heads can occur number of possible outcomes = Events are when the outcome of one event does have an effect on the outcome of the next event. Drawing two marbles in a row from a bag without replacing the first marble are events. bag contains 3 blue and 5 red marbles. Find the probability of drawing 2 blue marbles in a row without replacing the first marble. 5. The total number of marbles in the bag is. There are blue marbles in the bag. P(blue marble on first draw) = 6. There are now marbles in the bag. If you drew a blue marble on the first draw, there are blue marbles left in the bag. P(blue marble on second draw) = 7. P(blue, blue) = P(blue on st draw) P(blue on 2nd draw) = = Original content Copyright by Holt McDougal. dditions and changes to the original content are the responsibility of the instructor. 56 Holt McDougal Mathematics

6 -6 Challenge Pascal s Triangle special pattern, called Pascal s Triangle, can be used to find some probabilities. The triangle is called Pascal s Triangle because Pascal was one of the first mathematicians to formally study probability. Row Suppose 3 coins are flipped.. List all the possible outcomes. 2. How many outcomes show: all heads? 2 heads and tail? 2 tails and head? 3 tails? 3. How do the outcomes compare to row 3 of Pascal s Triangle? Find the probability of each event when flipping 3 coins heads? 5. 2 heads? 6. head? 7. 0 heads? Use Pascal s Triangle to find the following probabilities if 4 coins are flipped tails 9. 3 tails 0. 2 tails. tail 2. 0 tails 3. 2 heads Original content Copyright by Holt McDougal. dditions and changes to the original content are the responsibility of the instructor. 57 Holt McDougal Mathematics

7 -6 Reading Strategies Focus on Vocabulary When the outcome of one event does not affect the probability of the outcome of another, they are called in events. If you flip a coin once, it can land on head or tails. P(landing on tails) = 2 If you flip a coin a second time, P(landing on tails) is still 2. When the outcome of one event affects the probability of the outcome of another event, the events are called events. There are 52 cards in a deck, and 4 aces in the deck. P(drawing an ace) = 4 52 If an ace is drawn and not replaced, the probability of drawing an ace on the second draw drops to 3 out of 5. P(drawing another ace) = 3 5 Write events or in events to complete each sentence.. You roll a cube. Then you roll the cube a second time. 2. You take a coin from the jar and do not replace it. Then you take another coin from the jar. 3. One person in the class is chosen to be first in line. nother person is chosen to turn off the lights. 4. You have a bag with red, white, and blue counters. Explain how to conduct an experiment pulling counters from the bag so you will have in events. Original content Copyright by Holt McDougal. dditions and changes to the original content are the responsibility of the instructor. 58 Holt McDougal Mathematics

8 5. Explain how to change the experiment so the events are. -6 Puzzles, Twisters & Teasers Furry Math! Decide whether each event is or in. Circle the letter above your answer. Match the letters with the number of the problems to solve the riddle.. tossing a coin twice Q T in 2. spinning a spinner five times M H in 3. pulling two socks from a drawer at the same time E P in 4. drawing two marbles out of a bag at the same time O D in 5. throwing a pair of dice ten times X U in Which side of a rabbit has the most fur? 6. drawing two names out of a hat without replacement T in 7. picking cards from a deck without replacement S V in 8. spinning two different spinners two times K I in 9. throwing three coins three times D in 0. throwing one die five times U E in Original content Copyright by Holt McDougal. dditions and changes to the original content are the responsibility of the instructor. 59 Holt McDougal Mathematics

9 Original content Copyright by Holt McDougal. dditions and changes to the original content are the responsibility of the instructor. 335 Holt McDougal Mathematics