BS-2 | BUSINESS STATISTICS-2 | UNIT-4 BAYES THEOREM | OU | SEMESTER-4 | ‎⁨‎⁨@shivanipallela⁩

Added: 2026-06-08

[00:00:00]So in unit number four we are discussing base theorem problematic topic. Okay. So how to identify whether the question is a base theorem or normal probability question. If in the question if you are finding the percentages or if they are saying that in a bold factory two visions are there company A and company B is there. Right. Right. This type of things if they are finding this you need to consider this question as a base theorem question. See this question mark in a four bolt factory there are machine of P Q and R how many machines are there three machines are there manufacturing respectively P is manufacturing 25% Q is manufacturing 35% and R is manufacturing 40%. Their output is five four and 2 percentage that is 5% for P 4 percentage for Q 2 percentage for R. A bolt is drawn at random and it is known as defective.

[00:01:03]There was drawn the random defective bolt and it was defective. It seems what is the probability that is it was manufactured by machine 3 QR.

[00:01:14]So okay. So any type of base theorem question you need to write this statement. For example, how many machines are there? Three machines are there. So let us assume A1 as the machine one.

[00:01:40]A1 machine.

[00:01:44]Let us assume A2 as the machine Q A2. Next R is also there. A3 is we will assume as a machine R.

[00:02:03]Two missions go A1 and A2. That's it.

[00:02:07]Three missions A1, A2, A3. Four missions A1, A2, A3 and A4. How many missions are there? That you need to understand the A1, A2 and A3. After that, what is the percentages they have given?

[00:02:21]25%, 35% and 40%. The first percentages whatever you are having in your question that will become P of A1. What is the P of A1 percentage? 25%. Yes 25% 25% is nothing about the decimal format convert that is 25 divided by 100 if you do mean how much you'll get 0.25 you will get see 25 divided by 100 how much you getting 0.25 25. Next P of A2 how much percentage they have given 35%. 35% decimal format will convert just 35 divided by 100 is nothing about 0.35.

[00:03:10]Yes. Next you are having 40%. P of A3 is nothing about 40%.

[00:03:18]Or 40 divided by 100. If you do mean 0.4 4 0. Yes. A question. Now whatever the base theorem question, how many machines are there? You need to understand A1, A2, A3. Or else A1, A2, how many machines are there? That many columns you'll get it here. Afterward, the first percentages will become P of A1. Second percentages will become this is the first percentages of machine 3. Yes.

[00:03:45]Afterwards also 5%, 4%, 2% also they are saying. Yes or no? That will become P of B A1. What is P of B A1? How much percentage they are giving? 5%. 5% decimal format converges. 5 / 100 is nothing about 0.05.

[00:04:09]How much you'll get? 5 / 100 if you do mean 0.05.

[00:04:13]Same like that only P of B A2. How much percentage they have given? 4% they have given. That means 4 divided by 100 0.04.

[00:04:28]Clear? Next 2% also they are giving no.

[00:04:32]So P of B A3 2% is nothing about decimal format 2 / 100 how much you'll get? 0.02.

[00:04:44]Clear? Clear? Yes.

[00:04:47]So when they are giving three machines, when they are giving three machines, we need to intersect the A value and B value. Okay, we need to intersect. What is the intersection formula? P intersection B. See here P P of A intersection B. When you will do this intersection with B means when in the question there are three machines. three missions percent of PA1 percent of B of A1 into P1 0.25 P of B1 0.05 yes so that is P of A1 0.25 into 0.05 05 how much is your answer m 0.25 into 0.05 you will get 0.0125 the answer P of B= Z A2= Z that is 0.35 into 0.04 JR clear 0.35 into 0.04 how much you'll get 0 >> 0.014 014 P of A3 that is 0.4 into 0.02 0.40 4 into 0 how much?

[00:06:21]>> 0.008 008.

[00:06:24]When we are doing this step, when we will do this step, when in the question there are three machines or three factories or three companies or three goods, that time we need to take this value as your second step. Third step action.

[00:06:46]Clear? After that you need to draw the table. In a table there are five columns. One is event column. Second one is probability column. Third one is conditional probability. Fourth one is probability joint probability. Fifth one is pass posterior probability. Yes. So events a b c nothing about pqr a1 a2 a probability.

[00:07:17]What is the percentages of P of BA1 P of BA2 percent 0.05 0.04 0.02 yes or no that will become your probability.

[00:07:32]So see here 0.05 0.04 0.02 Yes. What is the conditional probability they have given? Conditional probability is nothing about the percentages of that 5% 4% and 2%. Conditional probability percent 5 4 2 simply joint probability 0.05 into 5 0.05 5 into 5.2 >> 0 >> 25 0.04 into 4.16 >> 0.16 0.02 02 into 22 0 >> clear do total of this column a column the total J and D 0.25 plus 0.16 plus 04 how much you'll get 0.414 414.

[00:08:51]Clear this here.

[00:08:55]Next last column that is posterior probability column. What is the value here? 0.25. What is the total of this column? 0.414 that is 0.25 divided by 0.414.

[00:09:12]How much answer you'll get?

[00:09:16]0.25 divided by >> 0.25 divided by 0.414 0.6 You will get 0.60 you will get again 0.16 divided by 0.414 0.38 04 divided by 0.414 414 0.96.

[00:09:47]Yes. Just number divide.

[00:09:51]Yes. So last one. Therefore, the probability of getting defective from P P mission can is 0.60 6 Q miss 0.38 R miss 0.96 that's 12 miss intersection B this call A intersection B this call suppose if in the question only two mach has two machines machine one and machine into machine one first percentage is 40 second is 60 third is output is 3% 1%.

[00:10:48]Okay. So two two percentages they have given for the each machine. So we need to assume let us assume let assume machine one as A1. We are assuming machine one as a A1 and machine two as A2. So two machines A1 and A2 we are assuming it. After assuming it we have to calculate P of A1. Yes. What is the percentage of P of A1? 40% they have given 40% or decimal format of convergence. 40 divided by 100 is nothing about 0.40.

[00:11:36]Yes. So 0.40 is your answer. Next P of A2 how much percentage they have given 40% and 60%. So 60% or decimal format 60 divided by 100 is nothing about 0.60.

[00:11:56]Okay. Next percentage also they have given that percentages will become P of B A1 how much they have given 3%. 3% is nothing about 3 divided by 100 it will be become 3 divided by 100 is nothing about 0.03 03 yes same like previous one only clear next P of B A2 how much percentage they have given 1% 1% or 1 divided by 100 also if you do means 0.01 01 will become your answer. Yes. After this you need to draw the table. What is the factors? Even you are having a1 and a2.

[00:12:44]What is the first percentage total you are having? 0.40.60.

[00:12:49]That percentages I'm writing here in the prior probability 0.4 0.60 into why? Because there are only two factors not three machines. Yes. Next you're having 0.03 and 0.01. 01 0.03 and 0.01 simply when you want to join probability what you need to do this into this 0 40 into 0.03 if you do means how much you'll get 0.012 0.60 into 0.01 if you will do means 06 so what will be your total answer here 0.012 012 0.6. If you add means you'll get 0.018.

[00:13:38]Yes. So last column what we need to do?

[00:13:40]We need to divide with the total that is 0.012 divided by 0.018.

[00:13:48]You will get an answer of 0.67.

[00:13:51]Again 0.6 divided by 0.018.

[00:13:58]If you do mean you'll get an answer of 0.33.

[00:14:01]Yes. Therefore, the probability of getting from A1 or machine one is 0.67 67 from A2 or machine 2 it is 0.33 that's it. So like this you need to understand your base theorem question mark. Okay. I hope that you have got clarity. If you're having any further doubts let me know in the comment section. All the very best for your examination and preparation. See you all in next video. Bye-bye students.