PROBABILITY| DATA HANDLING|CHAPTER 4| EX4.2|CLASS8| COMPLETE EXPLANATION| INSIGHTFUL MATHS
PROBABILITY| DATA HANDLING|CHAPTER 4| EX4.2|CLASS8| COMPLETE EXPLANATION| INSIGHTFUL MATHS
Transcript
00:00Hello Everyone. Welcome to Insightful Maths. Thank you so very much for liking my videos
00:06and I hope the upcoming videos will help you too. So, in today's session, we are going
00:11to continue the chapter Data Handling Class 8. In the previous session, we have discussed
00:17how to understand, analyze, and make the circle or the pie chart. Today, we are going to understand
00:24the concepts of probability, the difference between chance and probability and we'll continue
00:30with exercise 4.2. Okay? So, please do not forget to watch the video till end and get
00:36the clarity on the concepts. So, let's start. So, let us understand the very basic terms
00:43which are chance and probability. So, what is the basic difference? Generally, these
00:49are used interchangeably, chance and probability. When we talk about a chance, this is used
00:56in the layman language, like in the general language or daily basis, we use what are the
01:02chances. For example, the chances it may rain today, the chances that we may get late to
01:08catch our train, we may get late to reach our school. These are all chances. But, when
01:15we are using the term probability, we are using it in context of a branch of mathematics
01:22which is statistics. It is more a kind of a formal term. Chances are very random, you
01:28know, you hardly can assign it a number. But, probability is something wherein we can assign
01:35a number to those chances. Okay? So, these words are generally used interchangeably and
01:42in probability, there is more certainty or more likelihood of happening of a particular
01:48outcome. Let us understand. Probability basically tells you the degree of uncertainty. I will
01:58just read the statement and then I will explain you. Probability tells you the degree of uncertainty.
02:05It measures the likelihood. Likelihood is again the term interchangeable to chance.
02:11It measures the likelihood that an event will occur. Now, we don't know what is an event,
02:16what is a likelihood. For example, there is a, let's say there is a dice. Okay? We all
02:23play Ludos and we all know how does a dice look like. How many numbers are there on this
02:29dice? There are the numbers from 1 to 6. So, if I throw a dice, the numbers may come
02:36out either 1, 2, 3, 4, 5, 6. So, what are all these? These all are your outcomes, the
02:46result. Okay? Now, I ask you, what are the chances of 7 coming here? It is absolutely
02:52zero because 7 is not there on the dice. So, in general terms, I will ask you chance. If
02:58I say probability, so that means I want you to give me the answer as a number. So, what
03:05is the degree? A particular number which I can associate to a particular event. Now,
03:11what is an event? These all are outcome and each outcome is an event. So, if I ask you
03:19in this particular scenario, these all are total 6 outcomes. So, if I ask you, tell me
03:25the events for getting an even number. So, what are the events for getting an even number?
03:352, 4, 6. These 3 events are there for getting an even number. What are the events for getting
03:43an odd number? 1, 3 and 5. These are the events for getting the odd number when I throw a
03:50dice. And what is all this? These are the outcomes. And this act of throwing the dice
03:59or maybe tossing a coin, these are known as a random experiment. Okay? If the result of
04:07the experiment, now what is a random experiment? If the result of an experiment is not known,
04:14result kya aayega, kya nahin aayega, humein nahin bata. This is known as just a random
04:20experiment. Okay? So, throwing a dice, tossing a coin, these are all experiments. Now, example
04:27this I have already explained you, the dice one. Now, outcome, when we do an experiment,
04:34there could be different results like I have discussed here. 1, 2, 3, 4, 5, 6. Or maybe
04:40when I tossing a coin, there may be either a head or a tail. Okay? Two results, two events
04:45or two outcomes are possible. So, there could be different results. These possible results
04:52of a random experiments are known as outcome. Jo bhi ye result hote hain, ye outcome hi
04:59hain. And each outcome is what? That is an event. It's mentioned here. Each outcome or
05:06the collection of outcomes of an experiment is known as an event. Okay? Ab nao, there
05:12is an example. There are two possible outcomes when we toss a coin. It's but obvious. We
05:19know how does a coin look like. There is a head and below that there is a tail. So, if
05:24I toss a coin, what, I mean what all results I can get? Either I can get a head or I can
05:32get a tail. So, there are only two outcomes. I may say either I can call it outcome or
05:40I may call it an event. Both are same. Okay? Alright? So, if every outcome, now there is
05:48another word, equally likely outcome. If every outcome has the same possibility of occurring,
05:57these outcomes are equally likely. That means sabki hone ka barabar barabar, there is a
06:03possibility that anything can come. Aisa nahi hai ek ki hone ka probability zyada hai, ek
06:09ki aane ka kam hai. There are equal probabilities or the equal measure, equal degree that anything
06:16can happen. So, these events are or these outcomes are equally likely. Or maybe in a
06:22general language I can say, in sabki hone ka chance is same. Hain na? Agar main coin
06:29ko toss karogi to head aane ka bhi jitna chance hai, utna hi tail aane ka bhi chance hai.
06:34Right? So, these two outcomes or events are equally likely. Now, next thing we need to
06:41understand how do we calculate the probability. Okay? Let us understand how do we calculate
06:48the probability. Humne abhi seekha event kya hota hai? Jo bhi outcome ka result hota hai,
06:54each result is an event. Theek hai? So, there is a probability formula, probability of let's
07:01say happening of an event A. Probability of happening of an event A, the number of favourable
07:09outcomes upon total outcomes. We will just do the examples or the questions based on
07:16this, you will understand this formula. Main ek baar aapko example se samjha deti hoon.
07:21If for example I have tossed a coin. So, either I will get a head or I will get a tail. Mujhe
07:28nikalna hai what is the probability of getting the head. Toh mera event kya hai yaha pe?
07:33Event I have taken head here. How many number of favourable outcome matlab? Jo mini question
07:39mein poochha gaya hai. You are a favourable kitne outcome mein aaye? Aap dekho mere paas
07:45only two outcomes are there. And how many outcomes are supporting head? Only one. So,
07:50my numerator is one. Denominator se is total number of outcome. Mere paas total result
07:56kitne aaye hai? Total toh two results hai. So, answer is one by two. One more very important
08:03thing that you need to know is, probability of any event, it always lies between zero
08:12and one. Probability ka answer will always lie between zero and one. Probability will
08:19be zero when an event is impossible. Abar main aapko bolu, after night what is the probability
08:27that morning will never happen? Answer is zero. Night ke baad morning hoga hi hoga.
08:33So anything which is impossible uska probability is zero. Anything which is hundred percent
08:40sure, okay, which is certain, uska probability will always be one. Toh jo hundred percent
08:46sure hai, probability is one. Jo hundred percent unsure hai, probability is zero. For rest
08:52other things, it will lie between zero and one. This you need to know. Another very important
08:59and interesting thing you should know that, probability of happening plus probability
09:06of not happening, that is always equal to one. Ab iska kya matlab hai? Adar main aapse
09:14poochu, what is the probability of getting ahead? Aapne nikala one by two. We have just
09:20done this. Now if I ask you, what is the probability that I am not getting ahead? Aap isme put
09:28karo, probability of happening the same event plus probability of not happening, it is always
09:34equal to one. Maine aapse not happening pooch hai, hai na? Toh probability of getting ahead
09:39kya tha? It was one by two. Probability of not getting ahead mujhe nahi pata, but I know
09:45the sum is always one. So what is this question mark, the probability of not getting ahead?
09:51It is plus one by two. If I take it to another side, it will be one minus one by two. And
09:58what is one minus one by two? It is one by two. That's your answer. Theek hai? It's very
10:03interesting. When we'll do the questions here, you'll be able to understand this better.
10:08So let us start doing question number one. It says, list the outcomes you can see in
10:15this experience. Bita hum se probability is not being asked. The only thing asked is the
10:21possible outcome. Ki kya kya result aasakta hai? Theek hai? Ab aap tekho question number
10:26one, A part. This is a wheel. If I spin this wheel, agar mein wheel po bhumati hai, so what
10:32all can come as a result, the possible outcomes? It can either be A, B, C, D and one more A,
10:41hai na? It is equally divided in how many parts? One, two, three, four, five. So total
10:46five outcomes are possible here. Theek hai? So what is the answer? List the outcomes you
10:53can see in these experiments. Answer here is, you have to repeat A two times. Do ba
10:59chance hai A aane ka and after that B, C and D. These are the total outcomes. Tossing the
11:07two coins together. Very interesting. Aap dekho, yeh mera first coin hai, yeh mera second
11:14coin hai. First coin pe I have the option head and tail dono hi honge. Second par bhi
11:20head aur tail dono hoga. Theek hai? Now, question is asking, if I am tossing two coins
11:25together, ek saath mein uchhali, toh different different kya the result aa sakte hai? That
11:30result is known as the outcome. Theek hai? Aap dekho, I am making the different combinations
11:35here. It's very interesting. Pehle hum head ko fix rakhte hai. On the first coin, it is
11:41head. Toh second pe kya aa sakta hai? Yeh wala maine fix kar diya, ke pehle coin par
11:46head hi aa raha hai. Second pe ya toh head aayega, yeh tail aayega. Let us write, first
11:51pe head, second head. Now, first head is fixed, ho sakta hai second pe tail aayega. Theek hai?
11:58Yeh option ho gaye, head ke saath humne combination banaya. Now, let us suppose, on first coin,
12:06the tail is coming. Aap tail ke saath kya different combination bana sakte hai? Again,
12:10the combination these two, tail ke saath ho sakta hai head aayega, tail ke saath ho sakta
12:14hai tail aayega. So, it can be tail-head, it can be tail-tail. So, how many outcomes
12:21are possible? 1, 2, 3 and 4 and that's your answer. Theek hai? So, the first one, head-head,
12:28head-tail, tail-head and tail-tail. Iske alaawa, there is no other chance, no other probability,
12:34no other combination is possible. Let's move to question number 2. When a die is thrown,
12:40theek hai? When a die is thrown, list the outcomes of an event of getting all this.
12:47Outcome of an event. Hum se answer, probability is not being asked, only the outcome. Result
12:53kya aayega? And provided this case is there. What is the probability? No, not probability,
13:00we are talking about just the outcomes. So, when we are tossing the dice. So, answer may
13:05be either 1, 2, 3, 4, 5, 6. Other than this, I am not going to get anything. A part is
13:12asking me, how many events, favorable events are there for getting a prime number. So,
13:19please identify how many prime numbers are there out of this. Is 1 a prime or composite?
13:26It is neither. It's neither prime nor composite. 2 is a prime number, 3 is a prime number and
13:335 is again a prime number. So, outcomes of getting, of an event of getting a prime number,
13:402, 3 and 5. Yeh saare wo outcomes hai when we are getting a prime number. B part now.
13:48The outcomes of the event of not getting a prime number. Theek hai? Prime number nahi
13:53hona chahiye. So, prime number kaun kaunse nahi hai? 1 bhi nahi hai, 4 bhi nahi hai,
13:596 bhi nahi hai. Answer of B part is 1, 4 and 6. See that the second part, A is asking you
14:09a number greater than 5. Greater than 5 means strictly greater than 5. Isme 5 se bada kaunsa
14:16hai? Only 6. Answer is 6 here. B part, a number not greater than 5. Not greater than 5 ka
14:24matlab 5 se bada nahi hona chahiye. Ho sakta hai equal to 5 ho, ho sakta hai less than 5 ho. There
14:30is nothing mentioned here. Bas ek cheez pata hai 5 se bada nahi hona chahiye. So, all these numbers
14:35are either equal to 5 or less than 5. So, answer should be 1, 2, 3, 4, 5. That's your answer for
14:44second one, B part. I hope you are able to understand till here. Let's move to question
14:49number 3. Find the probability. Now, you need to give the answer as a probability of a pointer
14:57stopping on D in question number 1, A part. The wheel was spinning. We are being asked,
15:05what is the probability, yeh jo pointer hai na, yeh wala pointer, what is the probability that
15:10pointer will stop on D? I told you already how to find the probability of an event. Probability
15:19of an event is the number of favourable outcomes divided by the total number of outcomes. Hamara
15:27favourable outcome kya hai? Favourable is D. Hume answer D chahiye. And how many total options are
15:34available? 1, 2, 3, 4, 5. Aap yeh nahi sochogi, A do ba repeat hua hai. Of course. But there are,
15:41this is included. It is covering two portions out of six. Theek hai? So, when we are spinning it up,
15:471, 2, 3, 4, 5. Out of these five boxes, the pointer can stop anywhere. So, you have to include
15:54this A two times. Theek hai? So, question number 3, A part. Probability of pointer stopping at D
16:03is how many favourable outcomes are there for D? D ek hi baar aa raha hai. Numerator is 1. And how
16:09many total outcomes are possible? 1, 2, 3, 4, 5. Answer is 1 upon 5. B part. The probability of
16:21getting an ace from a well-shuffled deck of 52 playing cards. Playing cards, dice, iski aur point.
16:31Many questions on probability or maybe different balls numbered isi ke aspas kumta rehta hai. So,
16:37you should be very well aware of, in a pack of 52 playing cards, how many ace, how many kings,
16:43how many queen, how many black card, how many red cards are there. So, I request, please go
16:49through the playing card once. It's there. It must be there at everybody's home. So, just go through
16:54it or maybe you can have a look online. If you people do not have it at home. Theek hai? Half
16:59of the cards are black. Half of the cards are red. Theek hai? In the black cards also, two kings are
17:05there. Two queens are there. Similarly, for the red cards, two kings and two queens are there.
17:11Right? And in four different kinds of cards, one ace is there. Ab hum se kya puch hai? The
17:17probability of getting an ace from a well-shuffled deck of 52 playing cards. Humein nikal lai.
17:24Probability of getting an ace. How many total aces are there in a pack of 52 cards? Total 4 aces
17:32are there. Numerator is 4. And how many total cards are there? Total cards are 52. Theek hai?
17:41Always ensure answer to be given in the simplest form. Like we always convert the fraction in
17:47simplest form. This has to be done likewise. This number 52 is divisible by 4. So, let us
17:54reduce it in the simplest form. 4 into 1 is 4. 4 into 1 is 4. 4 into 3 is 12. So, your answer is
18:021 upon 30. Okay? Coming to the C part. The probability of getting a red apple. Yaha pe dekho
18:12how many total apples are there? 1, 2, 3, 4, 5, 6, 7. So, total 7 apples are there. But what is
18:19the question asking me? The probability of getting a red apple. So, red is my favorable outcome.
18:26How many red apples are there? 1, 2, 3, and 4. So, probability of getting a red apple. 4 red
18:34apples are there. Out of total? Out of total 7. Answer is 4 upon 7. Moving on to question number
18:434. Numbers 1 to 10 are written on 10 separate slips. Theek hai? 1 se 10 tak humne alag-alag
18:50slip pe number lik diya. Now, they are kept in a box and mixed well. One slip is chosen from the
18:56box without looking into it. Now, you need to get the probability of all this. Ab aap dekho.
19:03Sabse pehle hum samajh jaate hain if the slips are numbered 1 to 10 and we are picking up a
19:08slip randomly. So, outcome kya kya ho sakta hai? Let us write all the outcomes here. Answer can
19:13or the outcome can be either 1, 2, 3, 4, 5, 6 or it can be 7, 8, 9, and 10. There are no other
19:23numbers other than this one in the jar. So, these are the final outcomes. Anything of this can come.
19:30Now, first part is what is the probability of getting a number 6? How many 6s are there?
19:37There is only one 6. Out of how many numbers? 10 numbers. So, answer probability of getting a 6.
19:46This is the answer for the first part. The probability of getting a 6 is 1 because we
19:53have only one 6 here. Out of how many? Out of 10 numbers. So, probability of getting a 6 is 1 upon
20:0010. Now, I request mute this video and do it yourself and then check the answer.
20:08Getting a number less than 6. Probability of number less than 6. Ab less than 6 mere
20:16paas kitne option hai? 1, 2, 3, 4, 5. There are 5 options less than 6. So, numerator has to be 5.
20:25Total how many outcomes are there? Total to 10 number the. So, it is 5 by 10. Do not forget to
20:33convert it to simplest form. And what is the simplest form of 5 by 10? That is 1 by 2. That
20:39is the answer for your second part. Moving to the third part now. Getting a number greater than 6.
20:48Greater than 6 means exactly greater than 6. We will not even include 6.
20:56So, greater than 6, the answer could be 7, 8, 9, 10. Only 4 options are available. So,
21:03for third part, probability of the number greater than 6. Greater than 6 with 4 options.
21:12And how many total outcomes are there? 10. It is 4 by 10. It has to be simplified.
21:192 into 2 is 4. 2 into 5 is 10. Your answer is 2 upon 5. Fourth one. Getting a one-digit number.
21:29Beta, if I write all the outcomes, 1, 2, 3, 4, 5, 6 and all this,
21:36there is only one number which is a two-digit number. Otherwise,
21:39all the numbers are one-digit. So, how many one-digit numbers are there? 1, 2, 3, 4, 5,
21:456, 7, 8 and 9. Okay? So, for fourth part, probability of getting a one-digit number is
21:53total one-digit number 9 out of 10. This cannot be simplified further. That's your answer.
22:00Moving on to question number 5. If you have a spinning wheel with three grain center.
22:07Green, green and green. Three grain centers are there. One blue sector is there and one
22:19red sector is there. What is the probability of getting a green sector?
22:263, 4 and 5. Total how many outcomes are possible? This is very important to understand.
22:45The possible results or the outcome. So, we have only five options here.
22:50One red and one blue. Total five. We are being asked the probability of getting a green sector.
22:59So, probability of green. How many sectors are green here? 1, 2 and 3. Out of total five sectors.
23:07That is the answer. Probability of getting a green sector. Now, you tell me, what is the
23:13probability of getting a non-blue sector? We will use the same formula.
23:33So, probability of non-green.
23:37Non-green.
23:45It can be either green or red. Total four options out of five. Answer is 4 by 5. Let us do it in
23:53some other manner that I told you previously. The probability of happening and non-happening
24:00always. Sum it up to one. So that you understand the application. Now, we are having three green
24:09sector, one red and one blue. This is being given. Probability of non-blue. Let us find what is the
24:21probability of blue. How many blues are here? Only one. Out of five. So, probability of getting
24:29a blue sector is 1 by 5. Probability of blue plus probability of non-blue.
24:44What is the probability of blue here? 1 by 5. 1 by 5 plus probability of non-blue. That is equal
24:52to what? This is plus 1 by 5. If I take it to another side, it will be minus. So, I can write
24:59probability of non-blue is 1 minus 1 by 5. These are unlike fractions. How do we subtract? I will
25:08just do it here. 1 can be written as 5 by 5. So, this minus 1 by 5. Take 5 common and 5 minus 1
25:19is 4. Is it not the same answer that we have got previously? Non-blue means it should not be blue.
25:29So, how many non-blue options are there? 4. Have a look. It is 4. And how many total options are
25:35there? 5. Answer is 5. Just 4 apart 5. I hope you are able to understand this. Now, only one part
25:44is left out. Question number 6. Please have a look. Find the probability of the events given
25:50in question number 2. We have thrown the dice. What is the outcome? 1, 2, 3, 4, 5, 6. These are
26:08the different events. We have to find the probability of getting a prime number. First one,
26:14probability of a prime number. How many prime numbers are here? 1, 2, and 3. Numerator is 3.
26:27How many total numbers are there? 6. So, it is 3 by 6. And if I simplify,
26:33answer is 1 by 2. Be positive. Probability of prime number plus probability of non-prime
26:47number. Probability of prime number is 1 by 2 plus probability of non-prime number is 1 minus
27:021 by 2. It can be 2 by 2. So, 2 minus 1. That is 1 and denominator 2. That's your answer.
27:13Probability of a number greater than 5. How many numbers are here greater than 5?
27:18Only one number 6. So, for second one, A part, probability of greater than 6. Only one number
27:28out of total 6. That's your answer. And the last one, a number not greater than 5.
27:39So, how many options are there? Only 5 out of 6. So, answer for the B part is probability of
27:48the number not greater than 5. It means less than or equal to 5. 5 upon 6. That's your answer.
27:57So, we have done all the questions from exercise 4.2. I hope you are able to understand it well.
28:05If yes, please do not forget to like and subscribe the channel
28:10and keep watching the videos. Thank you so much for watching. Take care.