Slide 1

Note to the Presenter Print the notes of the power point (File Print select print notes) to have as you present the slide show. There are detailed notes for the presenter that go with each slide. Slide 2 The Probability of Independent and Dependent Events 8.12 The student will determine the probability of independent and dependent events with and without replacement. Slide 3 Prerequisite Skills and Vocabulary Skills Making tree diagrams Understanding fractions, decimals, and percents Vocabulary Equally likely events or outcomes Sample space Slide 4 What do we mean by independent and dependent events? Independent events - the occurrence of one event does not affect the occurrence of the other. Dependent events - the occurrence of one event changes the probability that another event will occur. Slide 5 Independent Events: What is the probability of flipping a coin twice such that it comes up heads both times? The first flip landing on heads or tails does not affect whether or not the second flip will land on heads or tails. A tree diagram shows each possible outcome. Since only one path gives two heads, the probability of two heads is one out of four or 1/4. Slide 6 Independent Events Drawbacks to using tree diagrams They can get very big very quickly. They can take a long time to create. We would like to be able to determine the probability of two events without have to list out all of the possible outcomes. Determine each probability and multiply them together. Slide 7 Independent Events: What is the probability of rolling a three on a standard number cube and flipping a coin and getting tails? These two events are independent because the rolling of the number cube does not affect the flipping of the coin. A tree diagram shows each possible outcome. Twelve possible outcomes, and rolling a three and getting heads is one option, so we have a probability of 1/12. Slide 8 Dependent Events If we have a jar with two red marbles and three blue marbles, what is the probability that if we pick two marbles we will pick one red and one blue from the jar? If we do not put the first marble we pick back in the jar, what we grab first from the jar will affect the probability of our second pick. A tree diagram would be rather large for this problem having 20 branches. Slide 9 Dependent Events: If we have a jar with 2 red marbles and 3 blue marbles, what is the probability that we will pick one red and one blue? Slide 10 Once we pick the first marble, there are only four left. The size of our sample space has changed from 5 marbles to 4 marbles. The probability of picking a red marble first is 2/5. The probability of picking a blue marble second is 3/4. The product of these two probabilities is 6/20 or 3/10. What if we picked up the blue marble first and then the red marble? Does it affect the probability? Slide 11 Dependent Events If we draw two cards from a standard 52-card deck without putting the cards back in the deck, what is the probability they will both be jacks? The probability that one card is a jack is 4/52. Sample space size changes to 51 cards. The probability that the second card is a jack is 3/51. The product of these two probabilities is Slide 12 Are the events dependent or independent? (That is does the size of the sample space change or does it stay the same) 1. Two cards are drawn from a standard deck of 52 cards. (a) selecting two hearts when the first card is replaced (or put back) in the deck. (b) selecting two hearts when the first cards is not replaced (or put back) in the deck. (c) a queen is drawn, is not replaced, and then a king is drawn. (d) drawing two reds cards (with replacement) from a deck of cards. (e) drawing a black card and then drawing a red seven (without replacement) from a deck of cards. Slide 13 Are the events dependent or independent? (That is, does the size of the sample space change or does it stay the same?) 2. A bag contains 9 Snickers, 7 Milky Way, and 4 Three Musketeers candy bars. Determine whether the events are dependent or independent and then find the probability. (a) Drawing two Snickers, replacing the first candy bar in the bag before drawing the second candy bar. (You dont want a Snickers bar so you are trying to get a different kind.) (b) Drawing Snickers, setting it aside, and then drawing a Three Musketeers. (c) Drawing a Milky Way, replacing it, and drawing a Three Musketeers. Slide 14 3. Rolling a four and then a five on a 12-sided number cube. 4. Picking two green marbles out of a jar (without replacement) given that there are 10 green marbles and 8 blue marbles. Are the events dependent or independent? (That is, does the size of the sample space change or does it stay the same?) Slide 15 Discussion What did you learn from this session? How would you apply this to your classroom? What is still unclear? Comments and/or concerns?