List or describe the elements in the specified set. Poll Three people are asked their opini

List or describe the elements in the specified set. ...

Key Concepts

Combinatorial Analysis

Combinatorial analysis involves techniques for counting, arranging, and selecting elements from a set, especially when the arrangement or order is significant. It is crucial in determining the number of outcomes that satisfy specific criteria, such as having a minimum or maximum number of certain responses.

Counting Principle

The counting principle (or multiplication rule) is used to determine the number of possible outcomes in a multi-stage experiment. When each stage of an experiment has a certain number of independent outcomes, the total number of outcomes is the product of the number of outcomes at each stage.

Event

An event is a specific subset of the sample space that meets a defined condition or set of conditions. It involves selecting those outcomes that share a particular property that interests the analyst, such as achieving a certain minimum number of a specific response.

Sample Space

The sample space is the complete set of all possible outcomes of a probabilistic experiment. It includes every possible combination of responses or events that can result from the experiment. For instance, when multiple individuals each choose from a set of options, the sample space consists of all possible ordered tuples of those responses.

Transcript

00:01 So when we have to find the sample space of any given situation, we have to understand it is the collection of all possible outcomes.

00:14 So collection of all possible outcomes.

00:21 Now generally when we are dealing with statistics, the basics of mathematics should be very helpful.

00:29 So here we would really see how the concept of permutation and combination will help us.

00:40 So these are the key topics that we should be reading side by side.

00:46 Because the end of the day you will see how this concept will help us here.

00:50 So now the current situation we are checking with that there will be, there are three possibilities that regarding a situation, there is a political situation, statement on which people can give three kind of opinions.

01:06 Okay.

01:07 The first one will be in favor, right? so people can be in favor of that statement.

01:16 The second one will be opposed, right? so they may oppose whatever they're hearing.

01:25 And the third one will be kind of, you know, unbiased or neutral, undecided.

01:29 They have not decided it correct so if you see there can be any three of these so if you see with the current situation people can answer in these three ways now when we are trying to find out the sample space of this we have to think that how many ways we can get these three places filled up right so we start with a tree diagram but before we proceed with tree diagram we have to think that for each of the places how many options we can have we can have i.

02:22 Again, we will have three options.

02:26 I.

02:29 And yet again, i.

02:32 You.

02:33 That means what, say, think of, this is you.

02:36 This is your friend and this is another friend, right? so you can have any of these.

02:44 But that will not impact whatever this person is having to say regarding the statement, political statement and then again that will not impact here so you can think that they will have all these three people will have different possible combinations of these three things now how do we find that out well if we just assume that the first person has chosen i how do we get that done so we think i if the first person has chosen then the second person can either choose an i again so both of them are choosing i and i or the second person can choose a o and o or the second person can choose you correct i o you so if you think the results cannot be anything other than this given the first person has chosen i so now the same way for the second person choosing i this can again split into three what is this three this is nothing but the third person so this is the first person there's the second person and this is the third person so i or you same way you can see if the second person has chosen or even for that the third person could have been i, o, or you.

04:21 There would have been three possibilities.

04:23 And then in the same line, again, if the second person had chosen you, the third person could have been any of these three things.

04:34 Right.

04:34 So this way, if i count, how many answers are there? one, two, three, four, five, six, seven, eight, nine.

04:43 Right so that's why we will end up having three times nine correct because this is for i but remember even the first person can have i or o or you so for i if the branching if the branching is nine times then even for for even for o, there will be nine such branchings and for you again nine such branchings.

05:21 So now let us try to write the sample space over here.

05:25 So we will start with i and instead of first only trying it with commas, i will try to write it in a columnar way.

05:34 So let me just clear it out a little bit and then show you.

05:39 So we can start with, i will fix the first place as i.

05:43 So what will be the other two places? first, i and then i.

05:48 So it will be i, i, i, i, i, okay? then i, second person, first two places are fixed at i and i.

06:00 Okay, so i will make this also red, i and i, but the third place could be o and then you.

06:10 So it is i, i, i, you.

06:13 Then again for i we will change the second place at oh because whatever could have happened with i has happened already so now we are left with o so i o i again i o will be fixed so i o you correct so i and o are fixed so i o you now think of what will happen we have the third most option so i i i i correct the second person choosing you as the next option even for that here we have three options i or you now this is the beauty that in this way if you organize them there will be no repetition there will be no such repetition none of these will be seen so let us try to write for the first place now will change it will go to correct so we will have o then the first two places being i and i so first two are fixed at o i okay so this is o and u then the first place will remain fixed at o o okay so if the second person chooses o i o may second one is o.

07:35 So i o and then third person choosing as per i or you, right? you see, for the second person, three times i, three times o and now it will be three times you...

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