Probability Mutually exclusive and exhaustive events

Slides:



Advertisements
Similar presentations
Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide
Advertisements

U NIT : P ROBABILITY 9-7: P ROBABILITY OF M ULTIPLE E VENTS Essential Question: How do you determine if two events, A and B, are independent or dependent,
Probability Sample Space Diagrams.
1 Chapter 6: Probability— The Study of Randomness 6.1The Idea of Probability 6.2Probability Models 6.3General Probability Rules.
Conditional Probability and Independence Section 3.6.
Bell Work: Factor x – 6x – Answer: (x – 8)(x + 2)
Probability Rules l Rule 1. The probability of any event (A) is a number between zero and one. 0 < P(A) < 1.
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)
Probability Probability is the measure of how likely an event is. An event is one or more outcomes of an experiment. An outcome is the result of a single.
Conditional Probability Objective: I can find the probability of a conditional event.
Probability – the likelihood that an event will occur. Probability is usually expressed as a real number from 0 to 1. The probability of an impossible.
7.4 Probability of Independent Events 4/17/ What is the number of unique 4-digit ATM PIN codes if the first number cannot be 0? The numbers to.
Recap from last lesson Compliment Addition rule for probabilities
List one thing that has a probability of 0?. agenda 1) notes on probability 2) lesson 1 example 1, 2 Exercise 5-8 Problem set 1-3 3)start lesson 3.
5.1 Probability in our Daily Lives.  Which of these list is a “random” list of results when flipping a fair coin 10 times?  A) T H T H T H T H T H 
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) =
PROBABILITY (Theoretical) Predicting Outcomes. What is probability? Probability refers to the chance that an event will happen. Probability is presented.
INDEPENDENT EVENTS. Events that do NOT have an affect on another event. Examples: Tossing a coin Drawing a card from a deck.
Probability.
9-7Independent and Dependent Events 9-7 Independent and Dependent Events (pg ) Indicator: D7.
Introduction to Probability By Dr. Carol A. Marinas.
What is the probability of two or more independent events occurring?
Independent and Dependent Events. Independent Events Two events are independent if the outcome of one event does not affect the outcome of a second event.
I can find probabilities of compound events.. Compound Events  Involves two or more things happening at once.  Uses the words “and” & “or”
13-4 Probability of Compound Events. Probability of two independent events A and B. P(A and B)=P(A)*P(B) 1)Using a standard deck of playing cards, find.
Warm Up: Quick Write Which is more likely, flipping exactly 3 heads in 10 coin flips or flipping exactly 4 heads in 5 coin flips ?
Probability Quiz. Question 1 If I throw a fair dice 30 times, how many FIVES would I expect to get?
Independent and Dependent Events Lesson 6.6. Getting Started… You roll one die and then flip one coin. What is the probability of : P(3, tails) = 2. P(less.
How likely are you to have earned a “A” on the test?
How likely is something to happen..  When a coin is tossed, there are two possible outcomes: heads (H) or tails (T) We say the probability of a coin.
Section 5.3: Independence and the Multiplication Rule Section 5.4: Conditional Probability and the General Multiplication Rule.
When a normal, unbiased, 6-sided die is thrown, the numbers 1 to 6 are possible. These are the ONLY ‘events’ possible. This means these are EXHAUSTIVE.
Probability of Independent and Dependent Events 11-5.
Discrete Math Section 16.1 Find the sample space and probability of multiple events The probability of an event is determined empirically if it is based.
Section 9-7 Probability of Multiple Events. Multiple Events When the occurrence of one event affects the probability of a second event the two events.
LEQ: What are the basic rules of probability? 9.7.
Adding Probabilities 12-5
Probability.
Probability OCR Stage 6.
Chapter 6 6.1/6.2 Probability Probability is the branch of mathematics that describes the pattern of chance outcomes.
A casino claims that its roulette wheel is truly random
Statistics 300: Introduction to Probability and Statistics
Unit 5: Probability Basic Probability.
Probability of Multiple Events
13.4 – Compound Probability
MUTUALLY EXCLUSIVE EVENTS
From Randomness to Probability
True False True False True False Starter – True or False
A casino claims that its roulette wheel is truly random
Warm Up – 5/16 - Friday Decide if the following probabilities are Exclusive or Inclusive. Then find the probability. For 1 and 2 use a standard deck of.
Unit 1: Probability and Statistics
Compound Probability.
Unit 6: Application of Probability
Probability Simple and Compound.
Investigation 2 Experimental and Theoretical Probability
Probability.
What does it really mean?
getting a little more complicated
Mutually Exclusive Events
Probability Rules Rule 1.
Binomial Distribution
the addition law for events that are not mutually exclusive
Probability Tree Diagrams
Probability Conditional Probability
Probability Multiplication law for dependent events
Note 9: Laws of Probability
Types of Events Groups of 3 Pick a Card
Thursday 05/16 Warm Up 200 people were surveyed about ice cream preferences. 78 people said they prefer chocolate. 65 people said they prefer strawberry.
Compound Events – Independent and Dependent
Probability.
Presentation transcript:

Probability Mutually exclusive and exhaustive events GCSE Statistics Probability Mutually exclusive and exhaustive events

Mutually exclusive events (7.7) Events are mutually exclusive if they can not happen at the same time. A coin that is flipped can not come down heads and tails at the same time so the events ‘a head’ and ‘a tail’ are mutually exclusive. If two events A and B are mutually exclusive P( A or B) = P(A) + P(B) This is called the addition for mutually exclusive events For example, if the probability of A hitting a six off the last ball of a cricket match is 0.03 and the probability of B hitting or running a four off the last ball is 0.08 and four runs are needed to win the game, the probability of winning = P(A) + P(B) = 0.03 + 0.08 =0.11 The law may be extended to three or more events: P(A or B or C) = P(A) + P(B) + P(C)

We write this as P(A) + P(not A) = 1 Exhaustive events (7.8 – 7.9) A set of events is exhaustive if the set contains all possible outcomes. For a set of exhaustive events, the sum of the probabilities is one (∑p = 1) In particular the probability of an event happening + the probability of an event not happening = 1 We write this as P(A) + P(not A) = 1 For example, if a bag contains red yellow and green balls and the probability of getting a red ball is 0.4, the probability of getting yellow or green ball = P(not red) = 1 – 0.4 = 0.6

Independent events and the multiplication law (7.10) Two events are independent if the outcomes of one event does not effect the outcome of the other. For two independent events A and B, the P(A and B) = P(A) x P(B) This is called the multiplication law for independent events.

Your turn Exercise 7H page 273 Exercise 7I page 275