calculating probabilities of two events
play

Calculating probabilities of two events F OUN DATION S OF P - PowerPoint PPT Presentation

Sep 28, 2023 •205 likes •1.35k views

Calculating probabilities of two events F OUN DATION S OF P ROBABILITY IN P YTH ON Alexander A. Ramrez M. CEO @ Synergy Vision Independence Given that A and B are events in a random experiment, the conditions for independence of A and B

  1. Deck of cards example (Cont.) P ( Face card ) = P ( Club and Face card ) + P ( Spade and Face card )+ P ( Heart and Face card ) + P ( Diamond and Face card ) FOUNDATIONS OF PROBABILITY IN PYTHON

  2. Face card example in Python T otal probability calculation, FC is Face card in the code P_Club_n_FC = 3/52 P_Spade_n_FC = 3/52 P_Heart_n_FC = 3/52 P_Diamond_n_FC = 3/52 P_Face_card = P_Club_n_FC + P_Spade_n_FC + P_Heart_n_FC + P_Diamond_n_FC print(P_Face_card) The probability of a face card is: 0.230769230769 FOUNDATIONS OF PROBABILITY IN PYTHON

  3. Total probability FOUNDATIONS OF PROBABILITY IN PYTHON

  4. Total probability (Cont.) FOUNDATIONS OF PROBABILITY IN PYTHON

  5. Total probability (Cont.) P ( D ) =? FOUNDATIONS OF PROBABILITY IN PYTHON

  6. Total probability (Cont.) P ( D ) = P ( V 1 and D ) + ... FOUNDATIONS OF PROBABILITY IN PYTHON

  7. Total probability (Cont.) P ( D ) = P ( V 1 and D ) + P ( V 2 and D ) + ... FOUNDATIONS OF PROBABILITY IN PYTHON

  8. Total probability (Cont.) P ( D ) = P ( V 1 and D ) + P ( V 2 and D ) + P ( V 3 and D ) FOUNDATIONS OF PROBABILITY IN PYTHON

  9. Total probability (Cont.) P ( D ) = P ( V 1) P ( D ∣ V 1) + P ( V 2) P ( D ∣ V 2) + P ( V 3) P ( D ∣ V 3) FOUNDATIONS OF PROBABILITY IN PYTHON

  10. Damaged parts example in Python A certain electronic part is manufactured by three different vendors, V1, V2, and V3. Half of the parts are produced by V1, and V2 and V3 each produce 25%. The probability of a part being damaged given that it was produced by V1 is 1%, while it's 2% for V2 and 3% for V3. What is the probability of a part being damaged? FOUNDATIONS OF PROBABILITY IN PYTHON

  11. Damaged parts example in Python (Cont.) What is the probability of a part being damaged? P_V1 = 0.5 P_V2 = 0.25 P_V3 = 0.25 P_D_g_V1 = 0.01 P_D_g_V2 = 0.02 P_D_g_V3 = 0.03 FOUNDATIONS OF PROBABILITY IN PYTHON

  12. Damaged parts example in Python (Cont.) We apply the total probability formula P_Damaged = P_V1 * P_D_g_V1 + P_V2 * P_D_g_V2 + P_V3 * P_D_g_V3 print(P_Damaged) The probability of being damaged is: 0.0175 FOUNDATIONS OF PROBABILITY IN PYTHON

  13. Let's start using the total probability law F OUN DATION S OF P ROBABILITY IN P YTH ON

  14. Bayes' rule F OUN DATION S OF P ROBABILITY IN P YTH ON Alexander A. Ramírez M. CEO @ Synergy Vision

  15. FOUNDATIONS OF PROBABILITY IN PYTHON

  16. P(A and B) for independent events P ( A and B ) = P ( A ) P ( B ) FOUNDATIONS OF PROBABILITY IN PYTHON

  17. P(A and B) for dependent events P ( A and B ) = P ( A ) P ( B ) P ( A and B ) = P ( A ) P ( B ∣ A ) FOUNDATIONS OF PROBABILITY IN PYTHON

  18. P(A and B) for dependent events (Cont.) P ( A and B ) = P ( A ) P ( B ) P ( A and B ) = P ( A ) P ( B ∣ A ) P ( B and A ) = P ( B ) P ( A ∣ B ) FOUNDATIONS OF PROBABILITY IN PYTHON

  19. P(A and B) is equal to P(B and A) P ( A and B ) = P ( A ) P ( B ) P ( A and B ) = P ( A ) P ( B ∣ A ) P ( B and A ) = P ( B ) P ( A ∣ B ) FOUNDATIONS OF PROBABILITY IN PYTHON

  20. P(A and B) is equal to P(B and A) (Cont.) P ( A and B ) = P ( A ) P ( B ) P ( A and B ) = P ( A ) P ( B ∣ A ) P ( B and A ) = P ( B ) P ( A ∣ B ) P ( A ) P ( B ∣ A ) = P ( A and B ) = P ( B and A ) = P ( B ) P ( A ∣ B ) FOUNDATIONS OF PROBABILITY IN PYTHON

  21. Bayes' relation P ( A and B ) = P ( A ) P ( B ) P ( A and B ) = P ( A ) P ( B ∣ A ) P ( B and A ) = P ( B ) P ( A ∣ B ) P ( A ) P ( B ∣ A ) = P ( A and B ) = P ( B and A ) = P ( B ) P ( A ∣ B ) P ( A ) P ( B ∣ A ) = P ( B ) P ( A ∣ B ) FOUNDATIONS OF PROBABILITY IN PYTHON

  22. Bayes' rule P ( A ) P ( B ∣ A ) = P ( B ) P ( A ∣ B ) P ( A ) P ( B ∣ A ) ⟹ P ( A ∣ B ) = P ( B ) FOUNDATIONS OF PROBABILITY IN PYTHON

  23. Total probability P ( D ) = P ( V and D ) + P ( V and D ) + P ( V and D ) 1 2 3 FOUNDATIONS OF PROBABILITY IN PYTHON

  24. Total probability (Cont.) P ( D ) = P ( V and D ) + P ( V and D ) + P ( V and D ) 1 2 3 P ( V and D ) = P ( V ) P ( D ∣ V ) 1 1 1 P ( V and D ) = P ( V ) P ( D ∣ V ) 2 2 2 P ( V and D ) = P ( V ) P ( D ∣ V ) 3 3 3 P ( D ) = P ( V ) P ( D ∣ V ) + P ( V ) P ( D ∣ V ) + P ( V ) P ( D ∣ V ) 1 1 2 2 3 3 FOUNDATIONS OF PROBABILITY IN PYTHON

  25. Total probability (Cont.) P ( D ) = P ( V ) P ( D ∣ V ) + P ( V ) P ( D ∣ V ) + P ( V ) P ( D ∣ V ) 1 1 2 2 3 3 FOUNDATIONS OF PROBABILITY IN PYTHON

  26. Bayes' formula P ( A ) P ( B ∣ A ) P ( A ∣ B ) = P ( B ) FOUNDATIONS OF PROBABILITY IN PYTHON

  27. Bayes' formula (Cont.) Bayes' formula: P ( A ) P ( B ∣ A ) P ( A ∣ B ) = P ( B ) The probability of a part being from vendor i, given that it is damaged: P ( V ) P ( D ∣ V ) i i P ( V ∣ D ) = i P ( D ) FOUNDATIONS OF PROBABILITY IN PYTHON

  28. Bayes' formula (Cont.) Bayes' formula: P ( A ) P ( B ∣ A ) P ( A ∣ B ) = P ( B ) The probability of a part being from vendor i, given that it is damaged: P ( V ) P ( D ∣ V ) i i P ( V ∣ D ) = i P ( D ) P ( V ) P ( D ∣ V ) 1 1 P ( V ∣ D ) = 1 P ( V ) P ( D ∣ V ) + P ( V ) P ( D ∣ V ) + P ( V ) P ( D ∣ V ) 1 1 2 2 3 3 FOUNDATIONS OF PROBABILITY IN PYTHON

  29. Visual representation of Bayes' rule P ( V ) P ( D ∣ V ) 1 1 P ( V ∣ D ) = 1 P ( V ) P ( D ∣ V ) + P ( V ) P ( D ∣ V ) + P ( V ) P ( D ∣ V ) 1 1 2 2 3 3 FOUNDATIONS OF PROBABILITY IN PYTHON

Recommend

Probabilities and Expectations A. Rupam Mahmood September 10, 2015 Probabilities

Probabilities and Expectations A. Rupam Mahmood September 10, 2015 Probabilities

Probabilities and Expectations A. Rupam Mahmood September 10, 2015 Probabilities Probability is a measure of uncertainty Being uncertain is much more than I dont know We can make informed guesses about uncertain events

286 views • 26 slides
Where do the probabilities come from? Probabilities come from: Experts Data D. Poole

Where do the probabilities come from? Probabilities come from: Experts Data D. Poole

Where do the probabilities come from? Probabilities come from: Experts Data D. Poole and A. Mackworth 2019 c Artificial Intelligence, Lecture 10.1 1 / 6 Learning probabilities the simplest case Observe tosses of thumbtack:

643 views • 30 slides
Review: Probabilities DISCRETE PROBABILITIES Intro We have all been exposed to informal

Review: Probabilities DISCRETE PROBABILITIES Intro We have all been exposed to informal

Review: Probabilities DISCRETE PROBABILITIES Intro We have all been exposed to informal probabilities. However it is instructive to be more precise. The goal today is to refresh our ability to reason with probabilities in simple cases.

528 views • 8 slides
Formal Modeling in Cognitive Science Lecture 17: Sample Spaces, Events, Probabilities Steve

Formal Modeling in Cognitive Science Lecture 17: Sample Spaces, Events, Probabilities Steve

Sample Spaces and Events Probability of an Event Formal Modeling in Cognitive Science Lecture 17: Sample Spaces, Events, Probabilities Steve Renals (notes by Frank Keller) School of Informatics University of Edinburgh s.renals@ed.ac.uk 19

469 views • 17 slides
Machines running on random tapes and the probabilities of events by George Barmpalias joint work

Machines running on random tapes and the probabilities of events by George Barmpalias joint work

1/18 Machines running on random tapes and the probabilities of events by George Barmpalias joint work with Cenzer/Porter and Lewis-Pye February 2017, Dagstuhl Victoria University of Wellington Chinese Academy of Sciences 2/18 Run a

332 views • 18 slides
Calculating Derivatives There are two types of formulas for calculating derivatives, which we may

Calculating Derivatives There are two types of formulas for calculating derivatives, which we may

Calculating Derivatives There are two types of formulas for calculating derivatives, which we may classify as (a) formulas for calculating the derivatives of elementary functions and (b) structural type formulas. Alan H. SteinUniversity of

687 views • 44 slides
Conditional Probability Independent & Related Events An independent event happens the same

Conditional Probability Independent & Related Events An independent event happens the same

8/6/2014 Zach Laster University of Helsinki Probability The likelihood of something Probabilities are not guesses happening Rolling a d6 results in a 16.7% percent Statistics Models for predicting events chance of getting

411 views • 10 slides
Should we think of quantum probabilities as Bayesian probabilities? Carlton M. Caves C. M.

Should we think of quantum probabilities as Bayesian probabilities? Carlton M. Caves C. M.

Should we think of quantum probabilities as Bayesian probabilities? Carlton M. Caves C. M. Caves, C. A. Fuchs, R. Schack, Subjective probability and quantum certainty, Studies in History and Philosophy of Modern Physics 38 , 255--274

234 views • 21 slides
1 A simplified definition Example: Rolling a dice Let be the sample space of an experiment. A

1 A simplified definition Example: Rolling a dice Let be the sample space of an experiment. A

Outline Probabilities Conditional probabilities Bayes theorem Distributions Discrete Continuous Advanced Herd Management Distribution functions Probabilities and distributions Sampling from distributions Estimation

545 views • 10 slides
Calculating Derivatives There are two types of formulas for calculating derivatives, which we may

Calculating Derivatives There are two types of formulas for calculating derivatives, which we may

Calculating Derivatives There are two types of formulas for calculating derivatives, which we may classify as (a) formulas for calculating the derivatives of elementary functions and (b) structural type formulas. Formulas for Derivatives of

245 views • 3 slides
What Youll Wh ll Learn arn Today ay Ca Calculating the he PV PV of a a stream of

What Youll Wh ll Learn arn Today ay Ca Calculating the he PV PV of a a stream of

Valuing Streams of Payments Calculating Payments Aa Aaron Stevens EC1 EC171 71, 27 27 September 2011 1 What Youll Wh ll Learn arn Today ay Ca Calculating the he PV PV of a a stream of paym payment ents s of of equal

439 views • 13 slides
Reading, writing and calculating in the kitchen 1 Reading, writing and calculating in the kitchen

Reading, writing and calculating in the kitchen 1 Reading, writing and calculating in the kitchen

30 th June 2011 Reading, writing and calculating in the kitchen 1 Reading, writing and calculating in the kitchen 2 Practical lessons Practical lessons Theory lessons City & Guilds international 7065 Cookery & culinary arts COURSE

297 views • 27 slides
Paradoxes of probabilistic programming and how to condition on events of measure zero with

Paradoxes of probabilistic programming and how to condition on events of measure zero with

Paradoxes of probabilistic programming and how to condition on events of measure zero with infinitesimal probabilities (to appear at POPL21) Jules Jacobs Radboud University Nijmegen julesjacobs@gmail.com November 23, 2020 1 / 25

898 views • 75 slides
Calculating distributions Chung-chieh Shan Indiana University 2018-09-21 Calculating

Calculating distributions Chung-chieh Shan Indiana University 2018-09-21 Calculating

Calculating distributions Chung-chieh Shan Indiana University 2018-09-21 Calculating distributions executable meaningful Calculating distributions executable meaningful Id also like to address this concept of being fake or

713 views • 57 slides
Statically Calculating Secondary Thread Statically Calculating Secondary Thread Performance in

Statically Calculating Secondary Thread Statically Calculating Secondary Thread Performance in

Statically Calculating Secondary Thread Statically Calculating Secondary Thread Performance in ASTI Systems Performance in ASTI Systems Siddhartha Shivshankar, Sunil Vangara and Alex Guimares Dean alex_dean@ncsu.edu Center for Embedded

441 views • 32 slides
The Nitty-Gritty of Calculating Your Production Costs by Dale Lattz and Gary Schnitkey 1

The Nitty-Gritty of Calculating Your Production Costs by Dale Lattz and Gary Schnitkey 1

The Nitty-Gritty of Calculating Your Production Costs by Dale Lattz and Gary Schnitkey 1 Topics 1. Concepts for calculating costs Benefits of knowing your cost of production Averages from FBFM Basis for calculating costs

983 views • 44 slides
Comonotone lower probabilities for bivariate Introduction and discrete structures Comonotonicity

Comonotone lower probabilities for bivariate Introduction and discrete structures Comonotonicity

Comonotone lower probabilities for bivariate Introduction and discrete structures Comonotonicity for lower probabilities Building Ignacio Montes and Sebastien Destercke comonotone lower probabilities Conclusions University of Oviedo,

422 views • 26 slides
Stochastic Simulation Idea: probabilities samples Get probabilities from samples: X count X

Stochastic Simulation Idea: probabilities samples Get probabilities from samples: X count X

Stochastic Simulation Idea: probabilities samples Get probabilities from samples: X count X probability x 1 n 1 x 1 n 1 / m . . . . . . . . . . . . x k n k x k n k / m total m If we could sample from a variables

476 views • 47 slides
Stochastic Simulation Idea: probabilities samples Get probabilities from samples: X count X

Stochastic Simulation Idea: probabilities samples Get probabilities from samples: X count X

Stochastic Simulation Idea: probabilities samples Get probabilities from samples: X count X probability x 1 n 1 n 1 / m x 1 . . . . . . . . . . . . x k n k x k n k / m total m If we could sample from a variables

714 views • 18 slides
Partially specified Probabilities: decisions and games May 2007 Ehud Lehrer The problem

Partially specified Probabilities: decisions and games May 2007 Ehud Lehrer The problem

Partially specified probabilities Partially specified Probabilities: decisions and games May 2007 Ehud Lehrer The problem Partially specified probabilities Nash equilibrium implicitly assumes that each player knows what other players

653 views • 38 slides
N-Gram Model Formulas Estimating Probabilities N-gram conditional probabilities can be

N-Gram Model Formulas Estimating Probabilities N-gram conditional probabilities can be

N-Gram Model Formulas Estimating Probabilities N-gram conditional probabilities can be estimated Word sequences from raw text based on the relative frequency of word sequences. Chain rule of probability Bigram: N-gram: Bigram

413 views • 4 slides
Method for analytically calculating BER (bit error rate) in presence of non-linearity Gaurav

Method for analytically calculating BER (bit error rate) in presence of non-linearity Gaurav

Method for analytically calculating BER (bit error rate) in presence of non-linearity Gaurav Malhotra Xilinx Outline Review existing methodology for calculating BER based on linear system analysis. Link model with ISI, Crosstalk,

195 views • 17 slides
Logistic regression to predict probabilities SU P E R VISE D L E AR N IN G IN R : R E G R E

Logistic regression to predict probabilities SU P E R VISE D L E AR N IN G IN R : R E G R E

Logistic regression to predict probabilities SU P E R VISE D L E AR N IN G IN R : R E G R E SSION Nina Z u mel and John Mo u nt Win - Vector LLC Predicting Probabilities Predicting w hether an e v ent occ u rs (y es / no ): classi cation

1.01k views • 38 slides
STA 331 2.0 Stochastic Processes 4. Limiting Probabilities Dr Thiyanga S. Talagala August 25,

STA 331 2.0 Stochastic Processes 4. Limiting Probabilities Dr Thiyanga S. Talagala August 25,

STA 331 2.0 Stochastic Processes 4. Limiting Probabilities Dr Thiyanga S. Talagala August 25, 2020 Department of Statistics, University of Sri Jayewardenepura Markov chains: A Random Walk In-class 2 Limiting probabilities - Example Suppose

561 views • 15 slides

More recommend