Tuesday, May 1st Warm up Explain the difference between: experimental, theoretical, and compound probability Solve: 2x – 1 = -10 Write Down Math Homework Complete warm-up
Review Independent Vs. Dependent Tell whether each set of events is independent or dependent. Explain you answer. A. You select a card from a standard deck of cards and hold it. A friend selects another card from the same deck. Dependent; your friend cannot pick the card you picked and has fewer cards to choose from. B. You flip a coin and it lands heads up. You flip the same coin and it lands heads up again. Independent; the result of the first toss does not affect the sample space for the second toss.
Independent Probability You are multiplying fractions!
Example #1 Two Boxes each contain 4 marbles: red, blue, green, and black. One marble is chosen from each box. What is the probability of choosing a blue marble from each box? • Independent or dependent? • Probability in box 1? Probability in box 2? • Multiply the two events together! I
#2 You Try! An Experiment consists of spinning the spinner 3 times. • What is the probability of spinning a 2 all three times. • What is the probability of spinning an even number all three times. • 3 • 2 • 4 • 5 • 1
Practice Problems In your groups, find the probability of these compound events: 3. A coin is flipped 4 times. What is the probability of flipping 4 heads in a row. 4. An experiment consists of spinning the spinner twice. What is the probability of spinning two odd numbers? 5. An experiment consists of randomly selecting a marble from a bag, replacing it, and then selecting another marble. The bag contains 3 red marbles and 12 green marbles. What is the probability of selecting a red marble and then a green marble with replacement?
The probability of landing heads up is with each event. Answer #1 A coin is flipped 4 times. What is the probability of flipping 4 heads in a row. Because each flip of the coin has an equal probability of landing heads up, or a tails, the sample space for each flip is the same. The events are independent. P(h, h, h, h) = P(h) •P(h) •P(h) •P(h)
P(odd, odd) = P(odd) P(odd) • Answer #2 An experiment consists of spinning the spinner twice. What is the probability of spinning two odd numbers? The result of one spin does not affect any following spins. The events are independent. With 6 numbers on the spinner, 3 of which are odd, the probability of landing on two odd numbers is .
The probability of selecting red is , and the probability of selecting green is . Answer #3 P(red, green) = P(red) P(green)
Question of the day What do you think is going to change if we find the compound probability of dependent events?!?!
To determine the probability of two dependent events, multiply the probability of the first event times the probability of the second event after the first event has occurred. The DENOMINATOR in the second probability changes!
Important! You must assume that you got the first event!
Example #1 Suppose you draw 2 marbles WITHOUT REPLACEMENT from a bag that contains 3 purple and 3 orange marbles. 1. What is the probability of drawing a purple both times? 2. What is the probability of drawing a purple, then an orange?
#2 You Try! The letter in the phrase: I LOVE MATH are placed in a box. If two letters are chosen at random and without replacement, what is the probability that they will both be vowels? Raise your hand when you think your group has the correct answer!
#3 You Try Carmen drops 6 purple marbles, 5 black marbles and 3 orange marbles into a bag. Without looking, 2 marbles are chosen without replacement. What is the probability of choosing a purple and an orange?
What’s the difference? A bag contains 1 red, 7 black, and 2 yellow marbles. 1. Find the following probability when the marble is replaced after the first drawing. • P (red, then yellow) • P (black, then red) • P(black, black)_________ 2. Find the following probability when the marble is not replaced after the first drawing. • P(yellow, then red) • P (black, then not black) • P(yellow, then yellow)
Wednesday, May 2nd Warm up • Solve: 5x – 8 = -11 • When you flip a coin and roll a die, what is the probability of getting tales and a 5? Write Down Math Homework Complete warm-up
Example #1 License plates are being produced that have a single letter followed by three digits. All license plates are equally likely. Find the number of possible license plates. Use the Fundamental Counting Principal. second digit letter first digit third digit 26 choices 10 choices 10 choices 10 choices 26 • 10 •10 • 10 = 26,000 The number of possible 1-letter, 3-digit license plates is 26,000.
You try! 1. Employee ID codes at the mall contain 2 letters followed by 3 digits. Find the number of Possible ID Codes.
The Fundamental Counting Principle tells you only the number of outcomes in some experiments, not what the outcomes are. A tree diagram is a way to show all of the possible outcomes.
Tree Diagrams Finding outcomes……
All outcomes are listed on the RIGHT/VERY BOTTOM • A tree diagram is a way to show all of the possible outcomes.
Example #1 I have a photo of Sidney that I want to mat and frame. I can choose from a blue, purple, red, or green mat and a metal or wood frame. Describe all of the ways I could frame this photo with one mat and one frame. You can find all of the possible outcomes by making a tree diagram. There should be 4 •2 = 8 different ways to frame the photo.
The Tree Diagram Each “branch” of the tree diagram represents a different way to frame the photo. The ways shown in the branches could be written as (blue, metal), (blue, wood), (purple, metal), (purple, wood), (red, metal), (red, wood), (green, metal), and (green, wood).
You Try! A baker can make yellow or white cakes with a choice of chocolate, strawberry, or vanilla icing. Describe all of the possible combinations of cakes. You can find all of the possible outcomes by making a tree diagram. There should be 2 •3 = 6 different cakes available.
Tree Branch yellow cake white cake vanilla icing vanilla icing chocolate icing chocolate icing strawberry icing strawberry icing The different cake possibilities are (yellow, chocolate), (yellow, strawberry), (yellow, vanilla), (white, chocolate), (white, strawberry), and (white, vanilla).