Probability for Machine Learning source : https://en.wikipedia.org/wiki/Bayes%27_theorem#/media/File:Bayes_theorem_drugs_example_tree.svg Hi Folks !! In this post i will discuss about the tricks and tips that i use to solve questions based on probability and i will also discuss about where the concept of probability is used in Statistics and ML. Note: [ This post is on probability and probability only and not on ML Algorithms that uses probability. But I assure you, after reading this post you will feel confident in reading and understanding all the Probability based ML -Algo’s like — {Naive Bayes | Bayesian Statistics etc .. } or in Stats like — {Binomial Probability Distribution etc ]. So without wasting time, lets get started . Basics P(Event) = Favourable Outcomes / Total Possible Outcomes . Lets look at some examples: Formula => Means [1,2,3,4,5,6] ie. total possible outcomes = 6. What is the probability of getting 5 on throwing a dice ? Ans : 1 / 6 . Problem: Throwing a Dice (1 time ) — Means [Heads , Tails ] ie. Total possible outcomes = 2. What is the probability of getting a Head or Tail on tossing a coin? Ans: p(H)= 1/2 , p(T) =1/2 Problem: Tossing a Coin (1 time) — — Means total possible outcomes = number of balls in bucket . A bucket contains 10 green balls 7 blue balls and 3 white balls. You pick up a ball from basket (1 time) . What is the probability of getting a green ball ? Ans : 10 / (10 + 7 + 3) = 0.5 Problem: Bucket with different colour balls and you are selecting a particular colour ball Now lets make this thing a little interesting !!! What if i say, Throw 1 dice 10 times and find the probability of getting number ‘5’ exactly 7 times . Or Throw 5 dice together and find the probability of getting a sum 25 ?? [ Answer it in the comments section :) ] Tough huh !! Not really … To answer these questions you need to know few concepts . Lets look at them closely — Types of Events Mutually Exclusive events Two events are mutually exclusive if they do not occur at same time . Example : Head or Tail cannot occur at same time on tossing a coin. Question: Two dice are rolled what is the probability that the sum of numbers rolled is either 5 or 9 ? Ans : P(AUB) = P(A) + P(B) Independent Events Two events are independent when the result of one event does not affect the other . They both are pure independent events . Example: Tossing a coin 2 times one after the other are independent events . Question: two dice are thrown one after the other . what is a probability of getting an even on both dice ? Ans : P(A)*P(B) = 3/6*3/6 Dependent Events If the result of one event affects the result of other then both events are dependent. Example: A basket has 10 balls (5 Blue and 5 White) and you select the first ball and keep it aside and then you select another ball from the basket . Now, lets make a question out of point 2 . what is the P of getting blue both times ? Ans: P(A) * P(B,once A occurred ) = 5/10*4/9 P(AUB) = P(A)*P(B, once A has occurred) Conditional Probability This is based on the concept of dependent events , where probability that an event A takes place will depend on another event B. Conditional Probability of an Event B given A [represented by=> P(B/A)] Formula => P(B/A) = P(A and B intersection) / P(A) Example: Suppose, I wrote 2 post about “probability” on and found that 25% of viewers read both of my post and 42% of viewers read only my 1st post .Now, What percent of those viewers who read my 1st post also read my 2nd post? ANS : .25/.42 = P(1st intersection 2nd) / P(1st) = 60% = P(2nd/1st) ( I hope you got this one ). Hackernoon Bayes Theorem It describes the probability of an event, based on prior knowledge of conditions that might be related to the event. Formula : P(A/B) = P(B/A).P(A)/P(B) Bayes theorem and Conditional Probability question style are very much inter-related. What i mean is that you can easily convert a Bayes theorem question to a one on Conditional probability and Vice versa by just changing 1 line of the entire question . Lets Look an Example : Q. There are 2 basket with balls- and . Each basket contains and s . You select .What’s the probability of selecting a ? BASKET-A BASKET-B 3 blue balls 2 green ball 1 ball from a Basket Blue ball (Conditional Probability Question) Ans : Here, The Probability of picking Basket-A = 1/2 . Probability of picking Basket-B = 1/2 . Probability of selecting a Blue ball from Basket-A = 3/5 . Probability of selecting a Blue ball from Basket-B= 3/5 . P( Selecting Blue Ball ) = P(blue Ball, Basket-A is selected first ) + P(blue Ball , Basket-B is selected first ) Final Ans = 3/5*1/2 + 3/5*1/2 (I hope you got this) Converting the above conditional Probability Question into a Bayes !! Q. There are 2 basket with balls- and . Each basket contains and s . You select and What is BASKET-A BASKET-B 3 blue balls 2 green ball 1 ball from a Basket found that it’s a Blue Ball. the probability that its from Basket-A? (Bayes Question) P(Basket-A | Blue Ball )= P(Blue Ball | Basket-A)* P(Basket-A)/P(Blue Ball) P(Blue Ball ) = 3/5*1/2 + 3/5*1/2 (Calculated above in question) P(Basket-A) = 1/2 P(Blue Ball | given Basket-A is selected ) = 1/2*3/5 Final Answer ( Simply put values in formula )= (3/10 * 1/2 )/(6/10) You can also visualise the entire scenario by making a probability tree. (The image at the top) and then calculate evertyhing . Visualisation Tree for Bayes Theorem I hope you liked my post . Please give it a clap. It would encourage me to write more . If you are new to ml or Data Science, feel free to read my other post on machine learning by clicking on the link below . _Metrics is used to judge and compare the performance of machine learning models. It directly influences the type of ml…_medium.com Evaluating ML Models Once Again, thank you for reading my post and don’t forget to Clap Share and Follow ..
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