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

1 2 3 4 5 6 1 2 3 4 5 6 Vocabulary 6.16 (handout) pg Pg Practice 6.16 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. Event –A specific outcome or type of outcome. Possible Outcome –all the possible events in a probability experiment Simple Probability- One event occurring 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) …so…………… 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. Example like 0/8 means if you have 4 black, 2 blue, and 2 red socks, the probability of choosing yellow is 0/8 or 0. – A probability of 1 means the event will always occur. Example 5 out of 5 ( 5/5) chance means 1….like all blue socks to choose from.   Probability can be expressed as a fraction, decimal, or percent. 0 25% 50% 75% 100% Complete the number line with CERTAIN (100%), LIKELY (>50%), UNLIKELY (<50%), IMPOSSIBLE (0%) or use the chart on page 452 in book and graphing probability on a number line from 0-1 with specific examples. Pg Practice 6.16 Simple Probability There are 4 blue socks, 2 yellow socks, 6 red socks, and 2 green socks in a drawer. Make a representation of the data B B B B Y Y R R R R R R G G What is the probability of choosing a green sock? 2 14 What is the probability of choosing a white sock? 0 14 Independent Events Probability of rolling a 6 on one number cube and a 3 or a 5 on the other? 1 2 3 4 5 6 1 2 3 4 5 6 1 6 X 2 6 = 2 36 = 1 18 Dependent Events Probability of choosing a blue marble and then a green marble. DON’T FORGET TO SUBTRACT OUT THE MARBLE YOU REMOVED! B B B Y R R G G B B B Y R R G G 𝟑 𝟖 X 𝟐 𝟕 = 6 56 = 3 28

Something is taken away Pg 6.16 Independent Events Nothing is taken away 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 Something is taken away 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 R (1/7)(1/6) = 1/42 O Y B Pink F D P G D B 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