Presentation on theme: "6.16 The student will compare and contrast dependent and independent events and determining probabilities for dependent and independent events."— Presentation transcript:
1 6.16The student will compare and contrast dependent and independent events and determining probabilities for dependent and independent events.
2 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 experimentSimple Probability- One event occurring in a probability experimentIndependent Events - When one event is not affected by a second eventSpin 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= 1/6Dependent 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 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.% % % %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 6.16Simple ProbabilityThere are 4 blue socks, 2 yellow socks, 6 red socks, and2 green socks in a drawer.Make a representation of the dataB B B B Y Y R R R R R R G GWhat is the probability of choosing a green sock?What is the probability of choosing a white sock? 0 14Independent EventsProbability of rolling a 6 on one number cube and a3 or a 5 on the other?X = 2 36 = 1 18Dependent EventsProbability 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 G𝟑 𝟖 X 𝟐 𝟕 = = 3 28
3 Something is taken away Pg Independent EventsNothing is taken awayProbability 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 36Your Turn-Probability of spinning a blue on Spinner A and spinning a red on Spinner B?Spinner A Spinner B F D PProbability of tossing a heads on the coin and spinning a green or blue on the spinner?F D P6.16 Dependent Events PgSomething is taken awayThese 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 probability.Next, since you took one out there are only six left, so the probability of choosing a yellow is 1 6R(1/7)(1/6) = 1/42O YB Pink F D PG D BYour Turn-What is the probability of choosing a Reeses and then choosing a Kit Kat?F D PYBGRYBGR