Binomial distribution probability (solve with easy steps)

[Music] [Applause] [Music] as opposed to demo topic is binomial distribution so first we will see the formula so P of X equal to small X that is MC X P raise to X Q raise to n minus n now this understands the terms of the formula so first term is n now n means is the finite value and it is always the total example we can have thousand books so ever any thousand similarly there can be 10 pens or 15 bulbs so these are nothing but else or second term is piece and third term is Q so P always made success whereas Q means failure and this relation between this shoe is P plus Q equal one now X X means if this term we have to find it from quotient and it is present in last line of the question so let us understand this by an example so the question is if 10% of pens manufactured by a company are defective then find probability that a box containing two elephants contains exactly to do defective pants second question is at least two different events exactly means equal to two at least means two and more so let's see how to solve it first we have to find the parameter so the first parameter was N and N means the total number you can see total is two elephants so n is equal to 12 second was to find P now here P means the pens are defective supima means defective and the probability is 10% so 10 by hundred that is 1 by 10 then what is Q Q is 1 minus P that is 9 by 10 now we have our basic like n PQ we have now we need X now X what's on the question so we have to position 1 and 2 so first question we have to say P of X equal now yet exactly two pens are defective so X value equals 2 now substitute in this formula the formula was NC X P raise to X Q raise to n minus X so n is 2 L see X is 2 P is 1 by 10 again X is 2 Q is 9 by 10 and n minus X is 2 and minus 2 that is strength after pondering this you will get the answer now talking about the second addition the second condition is at least 2 defective pen now at least means P of X first it should be equal and greater so greater than equal to 2 which is nothing but 1 minus V of X less than two now it can be written as 1 minus P of X equal 0 plus P of x equals 1 let's take another example so the example 2 is probability that at any moment one telephone line out of 10 will be busy is 0.2 find probability that filing charges now first we have to find the parameter and P and Q n means the total so there are total 10 telephone lines P means the probabilities now here we consider P as the BB so the probability of line being busy is 0.2 so what will be Q Q is 1 minus P that is 0.8 so we are done with step one that is finding this term for the formula second is what is the condition that is finding X now the question is this find probability that Phi is our vision so P of x equals 5 and now using the formula that is n CX P - 2 X Q raise to n minus X n is del CX is our PI probabilities 0.2 again X is 5 Q is 0.8 and n minus X is n minus 5 after solving this we get the answer now let's see the properties of binomial distribution so the first is expected value or it is also called as mean that is nothing but n into P now second second is variance variance is represented as Sigma square that is n P Q so standard deviation is root of NPQ so the difference between Bernoulli and binomial distribution whimpers like bird lolly was for one like one coin one time it was very simple like it for it was for one but binomial is called and like ten books or less than 110 pens that's why the term ends in binomial is very important to friends other up community of persons are you then to like this video share with your friends and subscribe to my youtube channel so make the hair ugly video my till then take care this is Shane again without

Channel: Shrenik Jain

Views: 657,532

Keywords: Binomial distribution probability, Binomial distribution, Binomial, probability distribution., probability, random variables, maths, probability and statistics, binomial sums, binomial examples, solve step for binomial probability, step by step binomial distribution, easy steps in binomials, probability distribution videos, probability distribution tutorials, distribution in probability

Id: vqojqDds_eo

Length: 7min 31sec (451 seconds)

Published: Wed Mar 01 2017