WOULD YOU PLAY THIS GAME? Roll a dice, and win $1000 dollars if you roll a 6.

Slides:



Advertisements
Similar presentations
Probability Three basic types of probability: Probability as counting
Advertisements

Clear your desk for your quiz. Unit 2 Day 8 Expected Value Average expectation per game if the game is played many times Can be used to evaluate and.
Take out a coin! You win 4 dollars for heads, and lose 2 dollars for tails.
5.1 Introducing Probability Objectives: By the end of this section, I will be able to… 1) Understand the meaning of an experiment, an outcome, an event,
Warm up 1)We are drawing a single card from a standard deck of 52 find the probability of P(seven/nonface card) 2)Assume that we roll two dice and a total.
Card Counting What is it, how does it work, and can I use it to pay for college? (and if it does work, do I even have to go to college?) Jeff O’Connell.
Random Variables and Expectation. Random Variables A random variable X is a mapping from a sample space S to a target set T, usually N or R. Example:
Games of probability What are my chances?. Roll a single die (6 faces). –What is the probability of each number showing on top? Activity 1: Simple probability:
Introduction to Probability. Probability Quiz Assign a probability to each event. 1. You will miss a day of school this year. 2. You will get an A in.
A Collaboration between: Los Angeles USD University of California, San Diego San Diego State University University of California, Irvine Preparing for.
Aim #10-7: How do we compute probability? Empirical probability applies to situations in which we observe how frequently an event occurs.
Section 16.1: Basic Principles of Probability
Probability And Expected Value ————————————
Expected Value.  In gambling on an uncertain future, knowing the odds is only part of the story!  Example: I flip a fair coin. If it lands HEADS, you.
Chapter 7 Expectation 7.1 Mathematical expectation.
Algebra1 Independent and Dependent Events
Using Tinkerplots Ruth Kaniuk Endeavour Teacher Fellow, 2013.
Fair Games/Expected Value
Probabilities of common Games How do I avoid bad bets?
Warm-up The mean grade on a standardized test is 88 with a standard deviation of 3.4. If the test scores are normally distributed, what is the probability.
What are the chances of that happening?. What is probability? The mathematical expression of the chances that a particular event or outcome will happen.
Lucky Candies Probability Game By: Laura Santa Maria Isabella Moreno.
Honors Precalculus: Do Now 1.) You are betting with your friend. Every time you flip heads, your friend pays you a dollar. Every time you flip tails, you.
Warm up: Solve each system (any method). W-up 11/4 1) Cars are being produced by two factories, factory 1 produces twice as many cars (better management)
Section 8.2: Expected Values
CONFIDENTIAL 1 Algebra1 Theoretical Probability. CONFIDENTIAL 2 Warm Up 1) choosing a heart. 2) choosing a heart or a diamond. An experiment consists.
TIMES 3 Technological Integrations in Mathematical Environments and Studies Jacksonville State University 2010.
Quiz Time! Clear your desk except for a pencil & calculator!
Dependent and Independent Events. Events are said to be independent if the occurrence of one event has no effect on the occurrence of another. For example,
Collecting Data and Expected Value
1.3 Simulations and Experimental Probability (Textbook Section 4.1)
Warm Up Find the theoretical probability of each outcome
Expected Value. Expected Value - Definition The mean (average) of a random variable.
Expected Value.
The Wonderful World… of Probability. When do we use Probability?
Not So Great Expectations! Which game do you think has the highest return per dollar?
6.5 Find Expected Value MM1D2d: Use expected value to predict outcomes. Unit 4: The Chance of Winning!
Probability.
When you studied probability in earlier lessons, you focused on probabilities of single events (for example, one draw of a card, or picking one cube from.
Introduction to Probability – Experimental Probability.
The Mean of a Discrete Random Variable Lesson
Billion Dollar Baby Game Created By: Timmy Drzewinski Edwin McCracken.
Have you ever played a game where everyone should have an equal chance of winning, but one person seems to have all the luck? Did it make you wonder if.
Find Expected Value.  A collection of outcomes is partitioned into n events, no two of which have any outcomes in common. The probabilities of n events.
Counting Techniques (Dr. Monticino). Overview  Why counting?  Counting techniques  Multiplication principle  Permutation  Combination  Examples.
Expected Value and Fair Game S-MD.6 (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). S-MD.7 (+) Analyze.
PROBABILITY DISTRIBUTIONS DISCRETE RANDOM VARIABLES OUTCOMES & EVENTS Mrs. Aldous & Mr. Thauvette IB DP SL Mathematics.
Probability Test Review (What are your chances of passing?)
The Law of Averages. What does the law of average say? We know that, from the definition of probability, in the long run the frequency of some event will.
In games of chance the expectations can be thought of as the average outcome if the game was repeated multiple times. Expectation These calculated expectations.
Lesson 96 – Expected Value & Variance of Discrete Random Variables HL2 Math - Santowski.
16.6 Expected Value.
Essential Ideas for The Nature of Probability
You Bet Your Life - So to Speak
Determining the theoretical probability of an event
BASIC PROBABILITY Probability – the chance of something (an event) happening # of successful outcomes # of possible outcomes All probability answers must.
Expected Value.
2. There are 3 red, 7 blue and 6 green marbles in a bag.
10.1 Notes Need to grab a packet from the back for notes
Multiply the probability of the events together.
Probability And Expected Value ————————————
10.1 Notes: Theoretical and experimental probability
Expected Value.
Probability And Expected Value ————————————
Created by _____ & _____
Investigation 2 Experimental and Theoretical Probability
Expected Value.
Probability.
Bellwork: 5/13/16 Find the theoretical probability of each outcome
Homework Due Tomorrow mrsfhill.weebly.com.
Presentation transcript:

WOULD YOU PLAY THIS GAME? Roll a dice, and win $1000 dollars if you roll a 6

PROBLEM: WHICH OUTCOME WOULD YOU BET ON?

Payout: Win $600 Payout: Win $150

ROLL A DICE 10 TIMES AND SEE WHICH EVENT WOULD PAY MORE ON AVERAGE Payout: Win $600 Payout: Win $150 Number RolledTally Amount won: Average: Amount won: Average:

FINDING THE THEORETICAL EXPECTATION Payout: Win $600 Probability = 1/6 Value = $600 Expectation = 1/6 x 600 =$100 Try: Payout: Win $150 Expectation = 3/6 x 150 =$75 The expectation of an event is the product of the probability of an event, and the value of that outcome.

INVESTIGATING EXPECTATIONS

EXPERIMENTAL MEAN When you perform an experiment where each outcome has a certain value, we can calculate the experimental mean or average outcome for that experiment Eg) You roll a dice and win $1 for every even number rolled, and $2 for every odd number rolled. Play this game 10 times and find your experimental mean value.

THEORETICAL MEAN The theoretical mean value, or expected value, denoted E(X), is calculated by multiplying the probability of each event and its value, then finding the sum of these expectations. Eg) You roll a dice and win $1 for every even number rolled, and $2 for every odd number rolled. Find the expected value of this experiment.

FIND THE EXPECTED VALUE: 1.You flip a coin. If you flip heads you win $1. If you flip tails you lose $1. 2.Roll a dice. If you roll a 6 you win $100, otherwise you lose $1. 3.Pay $2 to draw two cards from a deck. You win $10 if you draw two face cards in a row. 4.Which of these games seemed fair? How can you tell?

LUCKY DOUBLE 7/11 Rules of the Game: Roll two dice at the same time. If you roll a sum 7, 11 or doubles you win $10 dollars. You pay $2 dollars to play the game. Your task: - Simulate playing this game 100 times and calculate your experimental mean value - Calculate your theoretical mean value - Explain : Who would you rather be, the player or the operator?

LOTTO 6/49 A ticket costs $5. You pick 6 different numbers between 1 and 49. On the day of the draw, 6 random numbers are chosen. If they all match the numbers on your ticket (in any order) then you win $10,000,000 What is the expected value of buying a Lotto 6/49 ticket?

SUMMARY What is expected value? How is it different from an experimental mean value? What does it mean for a game to be mathematically fair? When will the experimental mean value and the theoretical mean value be close to each other? p. 374 #3, 4, 8, 10, 12, 18 Challenge: 13