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6.16

6.16. The student will compare and contrast dependent and independent events and determining probabilities for dependent and independent events. . Pg Practice 6.16 Sample Space

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6.16

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  1. 6.16 The student will compare and contrast dependent and independent events and determining probabilities for dependent and independent events.

  2. Pg Practice 6.16 Sample Space How many outfits (sample space) can you make from blue pants, tan pants, or black pants, and a red shirt or a yellow shirt, and tennis shoes or boots? TREE DIAGRAM CHART LIST Pants Shirts Shoes sum x sum x sum Independent Events Probability of rolling a 6 on one number cube and a 3 or a 5 on the other Dependent Events Probability of choosing a blue marble and then a black marble. DON’T FORGET TO SUBTRACT OUT THE MARBLE YOU REMOVED! Vocabulary 6.16 (handout)pg Sample space - The set of all possible outcomes in a probability experiment. Probability – The chance of an event occurring; expressed using a ratio. The numerator describes how many times the event will occur, while the denominator describes the total number of outcomes for the event. Outcome - Possible results of a probability event. For example, 4 is an outcome when a number cube is rolled. Ratio - A comparison of two numbers by division. Example: The ratio 2 to 3 can be expressed as 2 out of 3, 2:3, or 2/3. Tree diagram –A diagram used to show the total number of possible outcomes in a probability experiment. It iooks like a tree with branches. Event –A specific outcome or type of outcome. Possible outcome –all the possible events in a probability experiment independent events - When one event is not affected by a second event Spin two spinners. One has yellow, green, and blue. The other has only orange and purple. The probability of landing on yellow on the first spinner (1/3)and purple on the second is (½) is 1/3 • ½= 1/6 dependent events - The result of one event affects the result of a second event. There are six cookies. 2 are oatmeal, 3 are peanut butter, and 1 is sugar. Probability of choosing a peanut butter is 3/6. THEN choosing an oatmeal is 2/5 (because you took a cookie out). Multiply them and you have the probability of choosing a peanut butter and then an oatmeal cookie! 3/6 • 2/5 = 6/30 and simplified is 1/5…so a 20% chance *The probability of an event occurring is a ratio between 0 and 1. – A probability of 0 means the event will never occur. – A probability of 1 means the event will always occur.

  3. Pg 6.16 Independent Events Probability of rolling two number cubes and getting snake eyes (or any doubles for that matter)? There is a 1 in 6 chance for cube A and a 1 in 6 chance for cube B. (1/6)(1/6)= 1/36 Your Turn- Probability of spinning a blue on Spinner A and spinning a red on Spinner B? Spinner A Spinner B F D P Probability of tossing a heads on the coin and spinning a green or blue on the spinner? F D P 6.16 Dependent Events Pg These are a little tricky! Probability of choosing a red lollipop and then choosing a yellow lollipop? First, there are 7 lollipops. Choosing a red has a 1/7 probability. Next, since you took one out there are only six left, so the probability of choosing a yellow is 1/6 (1/7)(1/6) = 1/42 F D P Your Turn- What is the probability of choosing a Reeses and then choosing a Kit Kat? F D P Y B G R Y B G R

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