How to Calculate the Odds of Winning the Lottery

in this video lesson I'm going to talk about probability and lottery odds not long ago I came across a newspaper article and it read the lottery is our best hope say three and ten that means that 30% of people think the lottery is their best hope so in this video I'm going to talk about how to calculate the odds of winning the lottery using two different methods the first method is using combinations or a combination theory I guess to the equations and don't be frightened away by all the numbers and equations I'm gonna walk you through it step by step and the second method I'm gonna use probability theory which is the classic way so and again don't freak out I'm going to walk you through it step by step depending on the lottery there's a different number of balls that they choose and in this example I'm going to use 49 different balls and I will pick six different numbers there are a lot of different combinations picking six numbers at random from 49 different balls and that's what I'm going to do I'm account up or figure out how many different combinations so that's the first thing how many different combinations and we know that the numbers we picked initially that's just one combination so if we know we have one combination out of how many total possible combinations these represent one combination and the order of the numbers do not make a difference I'm gonna calculate how many different combinations so the first thing I know is N is equal to 49 that's the total number of balls and small case in or green n is equal to 6 that's tell me I'm gonna pick at one time number of balls picked so this is my standard equation now I'm gonna have just plug and chug so I take 49 factorial divided by 6 the green 6 factorial and then I take 49 again 49 minus let me squeeze through there 49 minus 6 close the parentheses and a factorial sign this simplifies to 49 factorial divided by 6 factorial I'll bring that over and I have 49 minus 6 which is 43 bring down the factorial sign and I multiply that times a 6 factorial now I could pound this out in the calculator but I'm gonna simplify it first you don't have to but I will share how to simplify it so this all equals 49 let me make my division line long there 49 times 48 times 47 times 46 times 45 times 44 times 43 factorial divided by 6 factorial times 43 factorial the 43 factorials cancel now if I multiply out the numerator I get 10 billion and something / / 6 factorial or 6 times 5 times 4 times 3 times 2 times 1 equal to 10 billion / 720 and this is equal to 13 million nine hundred and eighty three thousand eight hundred and sixteen that's the total number of combinations I can have with 49 balls picking six at a time so my total combinations was 13 million something and I started out with one combination so the chances of getting this one combination is one out of thirteen million nine hundred and eighty three thousand eight hundred and sixteen now I'm going to use standard probability theory this is exactly the same as the permutations I did with marbles without replacement so what's the probability of picking a green ball it's total picked out of total numbers and in this case it's six out of 49 so I pick one of the numbers one of the the green ones now I have the probability of picking the next number is a total picked divided by total numbers and this is the what's the total pick that's left over and it's going to be five so I have one two three four five numbers left over and so I'm going to move that five that's where that five comes from out of 48 so there's 48 numbers left over 2a so if I added up all those numbers is 48 total so it's five out of 48 and I'll bring that over there right there now I have the same equation again I have total picked total left picked out of total numbers and I have four left over right so I have four out of 47 let me bring that ball over I have again the same thing over and over again I hope you get the hang of it now I have three balls left three green balls left so it's three out of 46 not over now I have two out of 45 I'm gonna get there so I have two out of 45 I have two balls left and out of 45 total balls let me bring that one over so this ins this isn't so bad and now finally I have the last total picked out of total numbers I have one ball left out of 44 possibilities let me bring that ball now let me take all these numbers all these fractions right there and let's multiply them all together I'll multiply them all times each other and the numerator surprisingly is equal to 720 and the denominator is equal to that 10 billion number we came up with before and this is equal to one out of 13 billion nine hundred eighty-three thousand eight hundred sixteen so it calculates the same as the previous example and I do like it when a plan comes together and everything works out so sure the knowledge show the love Facebook Google+ Twitter questions and comments below and don't forget to subscribe because I'm always posting 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Channel: statisticsfun

Views: 562,262

Keywords: Probability, Combination, Permutations, Lottery Mathematics, Educational, David Longstreet, MyBookSucks

Id: _aBKxnUtIOk

Length: 8min 17sec (497 seconds)

Published: Fri Jun 22 2012