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Venn Diagrams

Venn Diagrams. Diagram used as a pictorial representative for a probability concept or rule. Venn Diagrams. Rolling one die, find P(greater than 3 AND odd). Greater than 3 Odd. 1. 4. 5. 3. 6. 2. P(greater than 3 and odd) = ____{5}_____ = 1

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Venn Diagrams

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  1. Venn Diagrams Diagram used as a pictorial representative for a probability concept or rule

  2. Venn Diagrams Rolling one die, find P(greater than 3 AND odd) Greater than 3Odd 1 4 5 3 6 2 P(greater than 3 and odd) = ____{5}_____ = 1 {1, 2, 3, 4, 5, 6} 6

  3. VennDiagrams Rolling one die, find P(greater than 3 OR odd) Greater than 3Odd 1 4 5 3 6 2 P(greater than 3 OR odd) = __{1, 3, 4, 5, 6}_ = 5 {1, 2, 3, 4, 5, 6} 6

  4. Complement The set of all outcomes in a sample space that are not included in the event Symbol- E’(sometimes written as E) _

  5. Complement When rolling a die, find the probability of rolling a number greater than 3 Greater than 3 1 4 5 3 6 2 Complement is everything in the sample space, that is NOT in the event P(E’) = ___{1, 2, 3}__ = 3 = 1 {1, 2, 3, 4, 5, 6} 6 2

  6. Complement Example: Find E, P(E) and P(E’) for each of the following: 1. Rolling a die and getting an even number 2. Selecting a card from a deck of cards and getting a diamond

  7. Complement Example: Find P(E) and P(E’) for each of the following: 1. Rolling a die and getting an even number E = even number P(E) = ___{2, 4, 6}__ = 3 = 1 {1, 2, 3, 4, 5, 6} 6 2 P(E’) = ___{1, 3, 5}__ = 3 = 1 {1, 2, 3, 4, 5, 6} 6 2

  8. Complement Example: Find P(E) and P(E’) for each of the following: 2. Selecting a card from a deck of cards and getting a diamond E = diamond P(E) = 13 = 1 52 4 P(E’) = 39 = 3 52 4

  9. Complement P (E) + P(E’) = 1 P(E) = 1 – P(E’) P(E’) = 1 – P(E)

  10. Empirical Probability Based on the observations obtained from an experiment*Actually doing the experiment Frequency of event E total frequency _f_ Σf P (E) = =

  11. Empirical Rule (Example) Fish Type # of times caught (f) Blue Gill 39 Red Gill 51 Crappy 30 ________ Σf = 120 _39 120 13 40 _f_ Σf f of Blue Gill total f = = = P(Blue Gill) =

  12. Subjective Probability Uses a probability value based on an educated guess or estimate, utilizing opinions and inexact information

  13. Subjective Probability Ex: After watching the students in the hallway between classes your English teacher states that about 15% of the students are in violation of the dress code.

  14. Law of Large Numbers As an experiment is repeated over and over, the empirical probability of an event approaches the classical (actual) probability of the event

  15. Classify the following statements as an example of classical, empirical, or subjective probability. Ex: After watching ducks at the pond, Lizzy decides that only about 10% of the ducks swim around alone. Subjective Probability

  16. Classify the following statements as an example of classical, empirical, or subjective probability. Ex: All 30 students in class flip a coin once and 20 of these students get tails. Empirical Probability

  17. Classify the following statements as an example of classical, empirical, or subjective probability. Ex: When Brandon plays Craps he has a 1/6 chance that he will roll a 7 on his first roll Classical Probability

  18. Find E, P(E) and P(E’) of the following: A single card that is selected from a deck of cards is a red 7 E = red 7 P(E) = _2 = 1 52 26 P(E’) = 25 26

  19. Section #1 For each example, draw a tree diagram labeling each “level” or event out to the left of the diagram. EX: Flipping a penny and flipping a quarter Start Flipping a penny Heads Tails Flipping a quarter Heads Tails Heads Tails

  20. Section #1 Start Heads Tails Heads Tails Heads Tails When the diagram is complete, use it to create a list of your sample space (all of your possible outcomes.) Sample Space: S = {HH, TH, HT, TT}

  21. Section #1 Possible outcomes flipping penny: { } Possible outcomes flipping quarter: { } Sample Space: S = { # of possible outcomes flipping penny:_____# of possible outcomes flipping quarter:____ Total number of outcomes in the sample space:____ Heads, Tails Heads, Tails HH, TH, HT, TT} 2 2 4

  22. Section 2: EX: Using numbers 1-10, find P(odd or greater than 7) List all of the odd numbers in the set : { }List all numbers in the set greater than 7: { } How many odd #’s are in the set?____How many #’s in the set are greater than 7?____ How many #’s in the set are both odd andgreater than 7 at the same time?_____ (Circle them) 1, 3, 5, 7, 9 8, 9, 10 5 3 1

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