Presentation on theme: "Warm Up Problem of the Day Lesson Presentation Lesson Quizzes."— Presentation transcript:
1Warm UpProblem of the DayLesson PresentationLesson Quizzes
2Warm UpWrite each answer as a fraction, as a decimal, and as a percent.A 1–6 number cube is rolled.1. What is the probability that an even number will result?2. What is the probability that the number will be prime?12, 0.5, 50%23
3Problem of the DayI have two coins in my pocket that total 30 cents. One of the coins is not a nickel. What are the coins?a quarter and a nickel (One coin is not a nickel, the other one is.)
4Sunshine State Standards MA.7.P.7.2 Determine, compare, and make predictions based on experimental or theoretical probability of independent and dependent events…Also MA.7.P.7.1
6Raji and Kara must each choose a topic from a list of topics to research for their class. If Raji’s choice has no effect on Kara’s choice and vice versa, the events are independent. For independent events, the occurrence of one event has no effect on the probability that a second event will occur.If once Raji chooses a topic, Kara must choose from the remaining topics, then the events are dependent. For dependent events, the occurrence of one event does have an effect on the probability that a second event will occur.
7Additional Example 1A: Determining Whether Events Are Independent or Dependent Decide whether the set of events are dependent or independent. Explain your answer.Kathi draws a 4 from a set of cards numbered 1–10 and rolls a 2 on a number cube.Since the outcome of drawing the card does not affect the outcome of rolling the cube, the events are independent.
8Additional Example 1B: Determining Whether Events Are Independent or Dependent Decide whether the set of events are dependent or independent. Explain your answer.Yuki chooses a book from the shelf to read, and then Janette chooses a book from the books that remain.Since Janette cannot pick the same book that Yuki picked, and since there are fewer books for Janette to choose from after Yuki chooses, the events are dependent.
9Check It Out: Example 1ADecide whether each set of events is independent or dependent. Explain your answer.Tara randomly draws a card from a deck of playing cards, looks at it, and puts it back in the deck. Jerry randomly draws a card from the same deck.The outcome of Jerry’s draw is not affected by Tara’s draw because she replaces the card. The events are independent.
10Check It Out: Example 1BThere are five prizes hidden in boxes labeled 1 through 5. Nelson chooses one, and then Melanie chooses one of the remaining four boxes.There are fewer boxes to choose from after Nelson’s choice, so the outcome of Melanie’s choice is affected. The events are dependent.
11P(A and B) P(A) P(B) = Probability of Two Independent Events To find the probability that two independent events will happen, multiply the probabilities of the two events.Probability of Two Independent EventsP(A and B)=P(A)P(B)•Probability ofboth eventsProbability offirst eventProbability ofsecond event
12Additional Example 2: Finding the Probability of Independent Events Find the probability of choosing a green marble at random from a bag containing 5 green and 10 white marbles and then flipping a coin and getting tails.The outcome of choosing the marble does not affect the outcome of flipping the coin, so the events are independent.P(green and tails) = P(green) · P(tails)13=2The probability of choosing a green marble and acoin landing on tails is16
13Check It Out: Example 2AYou draw a marble from a bag containing 3 red and 7 white marbles and then flip a coin. Find the probability for eachpair of events.drawing a red marble and getting headsThe outcome of choosing a marble does not affect thecoin toss, so the events are independent.P(red marble and heads) = P(red marble) P(heads)31012320==
14Check It Out: Example 2BYou draw a marble from a bag containing 3 red and 7 white marbles and then flip a coin. Find the probability for eachpair of events.drawing a white marble and getting tailsThe events are independent.P (white marble and tails) = P (white marble) P (tails)71012720==
15P(A and B) P(A) P(B after A) = Probability of Two Dependent Events To find the probability of two dependent events, you must determine the effect that the first event has on the probability of the second event.Probability of Two Dependent EventsP(A and B)=P(A)P(B after A)•Probability ofboth eventsProbability offirst eventProbability ofsecond event
16Additional Example 3: Finding the Probability of Dependent Events A reading list contains 5 historical books and 3 science-fiction books. What is the probability that Juan will randomly choose a historical book for his first report and a science-fiction book for his second?The first choice changes the number of books left, and may change the number of science-fiction books left, so the events are dependent.
17Additional Example 3 Continued 58There are 5 historical books out of 8 books.P(historical) =37There are 3 science-fiction books leftout of 7 books.P(science-fiction) =P(historical and then science-fiction) = P(A) · P(B after A)=58371556=Multiply.The probability of Juan choosing a historical book andthen choosing a science-fiction book is1556
18Check It Out: Example 3Juan’s mp3 playlist has 7 dance tracks and 3 rock tracks. What is the probabilitythat his player randomly selects a dance track followed by a rock track?
19Check It Out: Example 3 Continued 710P(dance) =39P(rock after dance) ==13P (dance and then rock) = P (dance) P (rock after dance)71013=730=
20Lesson Quiz for Student Response Systems Lesson QuizzesStandard Lesson QuizLesson Quiz for Student Response Systems20202020
21Lesson Quiz: Part IDecide whether each event is independent or dependent. Explain.1. Mary chooses a game piece from a board game, and then Jason chooses a game piece from three remaining pieces.2. Find the probability of spinning an evenly divided spinner numbered 1–8 and getting a composite number on one spin and getting an odd number on a second spin.Dependent; Jason hasfewer pieces from which to choose.316
22Lesson Quiz: Part II3. Sarah picks 2 hats at random from 5 bill caps and 3 beanies. What is the probability that both are bill caps?514
23Lesson Quiz for Student Response Systems 1. Decide whether the given event is independent or dependent, and then explain. Regina flips tails on a coin and rolls 5 on a number cube.A. independent; the outcome of tossing a coin does not affect the out come of rolling a number cube.B. independent; the outcome of tossing a coin affects the out come of rolling a number cube.C. dependent; the outcome of tossing a coin does not affect the out come of rolling a number cube.D. dependent; the outcome of tossing a coin affects the out come of rolling a number cube.23232323
24Lesson Quiz for Student Response Systems 2. What is the probability that Lupe will choose 2 apples from a bin of 10 apples, 8 bananas, and 7 oranges?A.B.C.D.24242424