Good afternoon! August 9, 2017.

Slides:



Advertisements
Similar presentations
MAT 103 Probability In this chapter, we will study the topic of probability which is used in many different areas including insurance, science, marketing,
Advertisements

Probability Sample Space Diagrams.
1 1 PRESENTED BY E. G. GASCON Introduction to Probability Section 7.3, 7.4, 7.5.
CONDITIONAL PROBABILITY and INDEPENDENCE In many experiments we have partial information about the outcome, when we use this info the sample space becomes.
GOAL: FIND PROBABILITY OF A COMPOUND EVENT. ELIGIBLE CONTENT: A PROBABILITY OF COMPOUND EVENTS.
Section 4.3 The Addition Rules for Probability
The Addition Rule and Complements 5.2. ● Venn Diagrams provide a useful way to visualize probabilities  The entire rectangle represents the sample space.
Chapter 6 Probabilit y Vocabulary Probability – the proportion of times the outcome would occur in a very long series of repetitions (likelihood of an.
Section 5.2 The Addition Rule and Complements
Academy Algebra II/Trig 14.3: Probability HW: worksheet Test: Thursday, 11/14.
Section 2 Probability Rules – Compound Events Compound Event – an event that is expressed in terms of, or as a combination of, other events Events A.
AP Statistics Chapter 6 Notes. Probability Terms Random: Individual outcomes are uncertain, but there is a predictable distribution of outcomes in the.
Special Topics. General Addition Rule Last time, we learned the Addition Rule for Mutually Exclusive events (Disjoint Events). This was: P(A or B) = P(A)
Chapter 1:Independent and Dependent Events
Lesson 6 – 2b Probability Models Part II. Knowledge Objectives Explain what is meant by random phenomenon. Explain what it means to say that the idea.
Review Homework pages Example: Counting the number of heads in 10 coin tosses. 2.2/
12.4 Probability of Compound Events. Vocabulary Compound Event: the union or intersection of two events. Mutually Exclusive Events: events A and B are.
Probability. Rules  0 ≤ P(A) ≤ 1 for any event A.  P(S) = 1  Complement: P(A c ) = 1 – P(A)  Addition: If A and B are disjoint events, P(A or B) =
Representing Data for Finding Probabilities There are 35 students 20 take math 25 take science 15 take both Venn Diagram Contingency table M^M.
Probability What’s the chance of that happening? MM1D2 a, b, c.
Probability.
Not a Venn diagram?.
Independent Events Lesson Starter State in writing whether each of these pairs of events are disjoint. Justify your answer. If the events.
Independent Events The occurrence (or non- occurrence) of one event does not change the probability that the other event will occur.
Warm-up 1)You roll a number cube once. Then roll it again. What is the probability that you get 2 on the first roll and a number greater than 4 on the.
Conditional Probability and the Multiplication Rule NOTES Coach Bridges.
Copyright © 2011 Pearson Education, Inc. Probability: Living with the Odds.
Introduction Remember that probability is a number from 0 to 1 inclusive or a percent from 0% to 100% inclusive that indicates how likely an event is to.
5-Minute Check on Section 6-2a Click the mouse button or press the Space Bar to display the answers. 1.If you have a choice from 6 shirts, 5 pants, 10.
Chapter 10 – Data Analysis and Probability 10.7 – Probability of Compound Events.
Section 5.3 Independence and the Multiplication Rule.
STATISTICS 6.0 Conditional Probabilities “Conditional Probabilities”
Not a Venn diagram?. Warm up When rolling a die with sides numbered from 1 to 20, if event A is the event that a number divisible by 5 is rolled: i) What.
Probability What is the probability of rolling “snake eyes” in one roll? What is the probability of rolling “yahtzee” in one roll?
Probability IIntroduction to Probability ASatisfactory outcomes vs. total outcomes BBasic Properties CTerminology IICombinatory Probability AThe Addition.
Conditional Probability 423/what-is-your-favorite-data-analysis-cartoon 1.
Essential Ideas for The Nature of Probability
Adding Probabilities 12-5
Samples spaces are _______________
Good morning! August 14, Good morning! August 14, 2017.
Lesson 10.4 Probability of Disjoint and Overlapping Events
Aim: What is the multiplication rule?
PROBABILITY Probability Concepts
CHAPTER 5 Probability: What Are the Chances?
10.7: Probability of Compound Events Test : Thursday, 1/16
Basic Probability CCM2 Unit 6: Probability.
Probability Probability theory underlies the statistical hypothesis.
Probability Part 2.
12.4 Probability of Compound Events
Smart Start A bag contains 5 blue marbles, 6 purple marbles and 3 green marbles. One marble is selected at a time and once the marble is selected it is.
Mutually Exclusive and Inclusive Events
Basic Probability CCM2 Unit 6: Probability.
Introduction Remember that probability is a number from 0 to 1 inclusive or a percent from 0% to 100% inclusive that indicates how likely an event is to.
Mutually Exclusive and Inclusive Events
10.1 Notes: Theoretical and experimental probability
Click the mouse button or press the Space Bar to display the answers.
Mutually Exclusive Events
Unit 6: Application of Probability
Addition and Multiplication Rules of Probability
Probability Simple and Compound.
CHAPTER 5 Probability: What Are the Chances?
Click the mouse button or press the Space Bar to display the answers.
Conditional Probability
Mutually Exclusive Events
Mutually Exclusive and Inclusive Events
Adapted from Walch Education
Addition and Multiplication Rules of Probability
Warm-Up #10 Wednesday 2/24 Find the probability of randomly picking a 3 from a deck of cards, followed by face card, with replacement. Dependent or independent?
Events are independent events if the occurrence of one event does not affect the probability of the other. If a coin is tossed twice, its landing heads.
Applied Statistical and Optimization Models
Presentation transcript:

Good afternoon! August 9, 2017

Bellringer 1. 4.25 x 5.2 = 2. 1.2 x 3.5 =

Concept Check ___Probability___ ___Venn Diagram___ ___Complement___ ___Independent___ ___Addition Rule___

Standard: MGSE9-12.S.CP.2 Understand that if two events A and B are independent, the probability of A and B occurring together is the product of their probabilities, and that if the probability of two events A and B occurring together is the product of their probabilities, the two events are independent. Learning Target: I CAN represent real world objects algebraically. I CAN communicate mathematically using set notation. I CAN make everyday decisions by understanding conditioned probability.

Experimenting With Probabilities

Vocabulary Independent – event does not affect the 2nd event Dependent – event does affect the 2nd event Mutually Exclusive – two events are mutually exclusive if they both cannot occur at the same time

Activity – Experiment 1 You roll two fair six-sided dice. What is the probability that a 4 is rolled with the first die?   What is the probability that a 4 was rolled on the second die? What is the probability that a 4 show on each die? P(4) = 1/6 = 0.166 P(4) = 1/6 = 0.166 P1(4)  P2(4) = 1/6  1/6 = 1/36 = .0278

Activity – Experiment 2 You pick two cards from a standard deck of 52 cards without replacing the first card before picking the second. What is the probability of a red suited card on the first draw?   What is the probability of a red suited card on the second draw, given that we got one on the first draw?  What is the probability that the cards are both red suited? Why are these two experiments different? P(RS) = 26/52 = 0.5 P2(RS) = 25/51 = 0.4902 P(both RS) = P1(RS)  P2(RS) = 0.5  0.4902 = 0.2451 In the first experiment, events are independent. Not so in the second – events are dependent.

Independent vs Dependent Events A and B are independent if the occurrence of either event does not affect the probability of the occurrence of the other event Events A and B are dependent if the occurrence of either event does affect the probability of the occurrence of the other event

Independent Examples What is the probability of rolling 2 consecutive sixes on a ten-sided die? What is the probability of flipping a coin and getting 3 tails in consecutive flips? P(6 and 6) = P(6)  P(6) = 1/10  1/10 = 1/(102) = 1/100 = 0.01 P(H and H and H) = P(H)  P(H)  P(H) = 1/2  1/2  1/2 = 1/(23) = 1/8 = 0.125

Dependent Examples What is the probability of drawing two aces from a standard 52-card deck? What is the probability of drawing two hearts from a standard 52-card deck? P(A1 and A2) = P(A1)  P(A2) = 4/52  3/51 = 12/2652 = 0.005 P(H1 and H2) = P(H1)  P(H2) = 12/52  11/51 = 132/2652 = 0.050

Venn Diagrams in Probability A  B is read A union B and is both events combined also seen as A or B A  B is read A intersection B and is the outcomes they have in common also seen as A and B Disjoint events have no outcomes in common and are also called mutually exclusive In set notation: A  B =  (empty set) A B A B Mutually Exclusive Intersection: A  B

Multiplication Rule: Independent Events If A and B are independent events, then P(A and B) = P(A) ∙ P(B) If events E, F, G, ….. are independent, then P(E and F and G and …..) = P(E) ∙ P(F) ∙ P(G) ∙ ……

Addition Rule: Disjoint Events If E and F are disjoint (mutually exclusive) events, then P(E or F) = P(E) + P(F) E F Probability for Disjoint Events P(E or F) = P(E) + P(F)

Addition Rule for Disjoint Events If events A, B, and C are disjoint in the sense that no two have any outcomes in common, then P(A or B or C) = P(A) + P(B) + P(C) This rule extends to any number of disjoint events

Mutually Exclusive Examples What is the probability of rolling a 6 or an odd-number on a six-sided die? What is the probability of drawing a king, queen or jack (a face card) from a standard 52-card deck? P(6 or odd) = P(6) + P(odd) = 1/6 + 3/6 = 4/6 = 2/3 = 0.667 P(K or Q or J) = P(K) + P(Q) + P(J) = 4/52 + 4/52 + 4/52 = 12/52 = 3/13 = 0.231

General Addition Rule For any two events E and F, P(E or F) = P(E) + P(F) – P(E and F) E F E and F Probability for non-Disjoint Events P(E or F) = P(E) + P(F) – P(E and F)

General Addition Examples What is the probability of rolling a 5 or an odd-number on a six-sided die? What is the probability of drawing a red card or a face card from a standard 52-card deck? P(5 or odd) = P(5) + P(odd) – P(5 and odd) = 1/6 + 3/6 = 4/6 = 2/3 = 0.667 P(R or FC) = P(Red) + P(FC) – P(RFC) = 12/52 + 26/52 – ( 6/52 ) = 32/52 = 0.6154

Summary and Homework Summary Events are independent if the occurrence of either event does not affect the occurrence of the other P(A and B) = P(A)  P(B) Events are dependent if the occurrence of either event does affect the occurrence of the other P(A and B) = P(A)  P(B|A) (remember for next lesson) Mutually exclusive events can’t happen at same time P(A or B) = P(A) + P(B) (P(A and B) = 0) Events not mutually exclusive P(A or B) = P(A) + P(B) – P(A and B)