Notes 9 Tree Diagrams Dependent Events Dependent Events

Notes #9 Tree Diagrams & Dependent Events

Dependent Events • What are Dependent Events? - When the outcome of the 1 st event DOES affect the outcome of the 2 nd event. Ex. - Drawing Cards - Picking candy from a bag and eating it. **ONLY works when drawn items are NOT returned or replaced**

How to know if an Event is Independent or Dependent? “Does the 2 nd event DEPEND on what happened during the 1 st event? ” NO Events are Independent YES Events are Dependent

Independent or Dependent? 1) Rolling a 2 on a dice then flipping a coin ANS: Independent 2) Picking a orange Skittle out of a bag and eating it, then picking a red Skittle. ANS: Dependent 3) Picking a Jack out of a deck of cards then selecting a ten out of the deck ANS: Dependent

Dependent Events I have a bag of jolly ranchers, 3 blue berry and 7 cherry flavors. I pick one candy out without looking, eat it and then pick out and eat a second sweet. What is the probability that I eat one blue berry and one cherry? Set-up 1. Assign Symbols to the Choices: C = Cherry. ; B: Blue Berry. 2. Determine Total Sum: 3 B + 7 C = 10 Jolly Ranchers 3. Determine Probability for each item (1 st Draw) P(C) = 7/10 or 0. 70 P(B) = 3/10 or 0. 30 4. Determine Probability for 2 nd Draw): Total # decrease by 1 & # of choices per flavor due to no replacement. P(B) = 2/9 P(C) = 6/9 5. Create Tree Diagram

EXAMPLE Prob of 1 st Draw P(B) = 3/10 or 0. 30 P(C) = 7/10 or 0. 70 1 st Candy KEY Cherry: C Blueberry: B 2 nd Candy 6 9 7 10 3 10 Prob of 2 nd Draw P(B) = 2/9 P(C) = 6/9 C P(CC) = 7 x 6 = 42 10 9 90 C 3 9 B 7 9 C P(CB) = 7 x 3 = 21 10 9 90 P(BC) = 3 x 7 = 21 10 9 90 B 21 21 42 7 + = = Or 0. 47 90 90 90 15 2 9 B P(BB) = 3 x 2 = 6 10 ANS: P(Blue Berry & Cherry) is 0. 47. 9 90