Full transcript of “INTRODUCTION TO PROBABILITY - OUTCOMES (4th) FOURTH QUARTER GRADE 7 MATATAG TAGALOG MATH TUTORIAL”. Click a timestamp to open the video at that moment. Need another video? Use the YouTube transcript generator.
0:02 [Musika] Hello everyone. Welcome to Matth Esip where we make math easier to understand with our free Tagalog tutorials. If you are new here, subscribe po para updated tayo sa ating mga lessons. To my fellow teachers, if you are interested with our PowerPoint presentations, we offer editable PowerPoint products to save your time in your lesson preparation. You can check the links below or message us on Facebook. All right, let's get started with our lesson for today. Ang title po ng lesson natin is introduction to probability, experiments, sample space, simple events, and outcomes. Our objectives for today based on our learning competencies are the following.
0:48 First, we will collect data from experiments. Second, express outcomes in words or symbols and represents outcome in tables or in graphs. And then lastly, we will be solving problems using the outcomes of experiments. Okay. So, without further ado, let's now begin. Let's define first what is probability. Okay, since this is your uh first lesson in grade 7 on probability, we have to define the meaning of probability. Okay, first probability is a branch of mathematics that studies uncertainty and chance. It deals with predicting possible outcomes of random events and is widely used in statistics, science, and real life decision making.
1:34 In short, probability is a measure of chance. Okay. So, meron po tayong diagram dito. So, uh the measurement can range from 0 to 1. Okay. Ang mine-measure po natin dito is yung chance. Ah kung gaano kalaki yung tsansa ng isang bagay ay mangyayari. So, it can be impossible because the measurement is zero, no? Or it can be certain and the measurement is 1. Yun lang po iyung range niya from 0 to 1. So, kapag dito naman po siya sa 0.25, 25 or here 1/4 around here ah we can call it unlikely no kapag gitna naman we can say equally likely o 0.5 or 1/2 yung chance na
2:20 mangyari and then we also have likely that is 0.75 75 or 3/4 no or somewhere around here we can just call it likely and then yung last po is yung certain or yung sure na mangyayari ang isang bagay now for the real application of probability in our life it can be from simple tossing of a coin up to predicting the weather so madami pa pong mga applications ang probability sa ating buhay and you are going to learn all this in the next grade levels pati yung pag-compute ng probability. But for now, we will just be having introduction to probability, yung mga key terms and how to determine the
3:06 outcomes. All right. The first key term here is the word experiment. Ano po ang experiment? An experiment is an action or process that leads to an outcome but the results cannot be precisely predicted. Okay, we have some examples here. Una, we have here tossing a coin. So pag nag-tos tayo ng coin, hindi po natin alam yung magiging result niya. What else? We have rolling a die. Pag nag-roll po tayo ng die, pwedeng madaming possibility yan na maging result or outcome. And then drawing a card. We don't know what we will be drawing from a deck of cards. Ito po lahat ay tinatawag nating experiment. Next, the keyword here is outcome. Ano po ba ang ibig sabihin ng outcome? Outcome is a possible result of a single trial of an experiment. Okay.
3:52 Halimbawa po 'pag nagtoss or nag-flip tayo ng coin, uh the possible outcome here can be head or tail or 'yung uh likod po ng ating coin wherein makikita natin dito sa Pilipinas, we can read Bangko Central ng Pilipinas. 'Yun po yung tail and we are going to express it the result using some words like head or tail or symbols like H or T. Okay, the next key term here is the word sample space. Ano ang sample space? This is the set of all possible outcomes in an experiment. So, gagamit po tayo ng notation letter S to represent sample space. Okay. Example po, we have here rolling a die. Ano po ba yyung mga
4:38 possible outcomes pag nag-roll tayo ng die? So, we have here six possible outcomes. It can be a 1, a 2, 3, 4, 5, and 6. And if we're going to represent this using a sample space, gagamit na po tayo ng listing method. We will use listing or roaster method. So ano po yan? Ganito po siya. Yung napag-aralan niyo dun sa topic natin about sets, we can make use of the capital letter S. Yung notation po ng sample space equals yung atin pong braces. And then sa loob is yung mga elements or yung mga outcomes. We have 1 2 3 4 5 6 that represent the number of dots in our
5:23 die. Okay. Here is the word event. Okay. Gagamit po tayo ng notation E, capital letter E to represent event. Ano po ang ibig sabihin ng event? Event means one or more outcomes of an experiment, a subset of the sample space. Okay. So galing po ito sa sample space. Example, we have here rolling a die and getting a five. Okay? Ibig sabihin pag nag-roll ka ng die, there are six possible outcomes. Pero getting a five is just one possible outcome. Okay? Yun na po iyung event. Next is rolling an even number on a die. Okay. So from a six uh outcomes 'yung sample space po natin, ilan po don ang even number? Okay. So we can have this
6:09 three. Okay? Pwedeng 2, 4 and 6. Okay? Yung mga naiwan po like 1, 3 and 5 hindi na po siya kasama dito because they are add numbers. So ang event lang po natin is yung mga even numbers. We have 1 2 3. Okay? Yun na po iyung events. Now, ano pong tawag natin sa mga elements na nasa loob ng ating subset? Ang tawag po natin sa mga yan ay favorable outcomes. Okay? The elements of an event are called favorable outcomes. Iyung 2, 4 and 6. Iyung five. Yun po yung mga favorable outcomes natin. Okay? Let's practice this terms using this activity. Okay? I-identify natin iyung experiment, iyung outcome,
6:55 iyung sample space and iyung event in the following situations. Okay? So, we will be answering this together. But if you want to try it on your own, pwede niyo naman pong i-pause ito and then you can just come back later, no? So, let's have number one. We have here a spinner consist of three colors. We have blue, red, and yellow. When spun, the result is blue. Okay. So, i-identify po natin ano ang experiment. Okay. The experiment here is 'yung spinning the spinner. Okay? And outcome is blue, red or yellow. Kahit alin po dito, pwedeng yun po yung magiging outcome niya. Now, if we're going to write the sample space, we have to do it in the listing or roaster method. So, we have here S is equ to blue, red, and yellow.
7:43 Okay? And yung event. Ano po yung specific na event na gusto nating mangyari? Sabi dito, "When span the result is blue." So yun po yung event. Getting a blue result. All right. So how do we write it? We can also use the letter E to represent event. E is equ to blue. Next one. Number two, we have here. Drawing a card randomly from a box containing cards numbered 1 to 10 and getting a number that is more than six. Okay. So ano po ang experiment dito? Okay. First experiment is drawing a card. Next, ano po yung mga pwedeng outcomes natin? Any number from 1 to 10. Yun po iyung mga possibility no ah
8:29 results. Okay. And next for our sample space we have here S is equal to the elements 1 2 3 4 5 6 7 8 9 and 10. And lastly for our event, ano po iyung specific na event natin dito? We have getting a number that is more than six. Okay? So what are the elements of our event? We can use letter E is equal to the elements 7, 8, 9, and 10. Okay, ito naman po yung mga number na more than six doon sa ating card from 1 to 10. Okay. Number three, we have here a box contains mixed fruits and vegetables. We have apple, banana, egg plant, mango, cabbage, potato, orange, and grapes. A
9:14 person picks one item at random. Now he got a vegetable. So ano po yung ating experiment? Picking an item from a box of mixed fruits and vegetables. Outcome: pwede pong getting a vegetable or a fruit. Okay? Lahat po ng mga nabanggit diyan, this can be the possible outcomes. And our sample space, we can identify or enumerate them one by one. So we have apple, banana, egg plant, mango, cabbage, potato, orange and grapes. And for our event, he got a vegetable. So in our uh sample space, ano po ba dito 'yung mga vegetables? We have here egg plant. What else? Cabbage. Ano pa po? Potato. Okay. Okay. Itong tatlong to lang po ang pwedeng maging
10:00 element ng ating event. Okay, let's now proceed to the next part of our lesson which is determining the outcomes of fun experiments. So, magbibigay lang po ako ng mga examples para po i-discuss sa inyo kung paano kunin yung mga outcomes ng mga experiments. Okay, let's now proceed with the first example. Okay, we have here two fair coins are tossed. Determine the sample space of the experiment. Let A be the event where the coins turn up the same. What are the favorable outcomes for A? Okay. So dito po in our problem, we have here two coins na naiitos. So let us determine yung mga outcomes by writing the sample space. And then yung event po natin dito
10:47 is ah two coins have the same result. Okay. Ano po 'yung mga favorable outcomes natin for event A? So kanina po 'yung notation natin for event is letter E. Pero kung sa problem na-specify po kung ano 'yung letter na gagamitin or kung ano yung notation na gagamitin, we follow the notation. So here A po yung ginamit. Okay. Now, I'm going to discuss to you two methods. Dalawang methods po kung paano natin isusulat yung mga outcomes or paano natin i-express yung outcomes. The first method here is what we call systematic listing. Ano po ba ito? Ililista lang natin yung mga possible na results or outcomes. Halimbawa, dalawang coin yung naitos.
11:32 Pwedeng ang possible outcome niyan is dalawang head. Okay. Therefore, we can write here head and then head. Okay. Ano pa po? Pwede ring isang head at saka isang tail. So we have head and tail. Pwede rin pong dalawang tail. So we can write here tail and another tail. And then lastly, ano pa po yung hindi natin naisusulat? Yes, we can also have tail and head. Okay? Tail and head. Ito lang po yung mga possible results or outcomes. Ito po yung tinatawag nating listing method or systematic listing. Ah meron po tayong sinusunod na ah pattern. Okay? Kaya po siya tinawag na systematic. Next one, we also have what
12:18 we call the three diagram method. Okay. Ito po is gumagamit tayo ng visual representation to uh write the possible outcomes. Okay? So we can divide it into two parts. Ung is first coin, no? Ano po 'yung possibility pag nag-tos tayo sa first coin? Dalawa lang po. We have H to represent head and then T. Letter T to represent tail. Pwedeng head or tail lang siya. And then for the second coin, magba-branch out po yan. So yung una pwedeng after masusundan po ulit ng either head or tail. Yung pangalawang coin masusundan din po yan ng head or tail dito sa tail ng first coin. Okay? So para siyang three. Nagba-branch out lang
13:04 siya. Therefore, our outcomes, we have here dalawang head. Okay? Head, head. That's why we have here 2h. We can also have here and tail. So H and T. Next, pwede rin pong tail and H or tail and head. So we have th And then lastly we can have tail and tail. Okay? So ito po yung dalawang method on how to write our possible outcomes. Now going back to the question. Sabi po dito, "What are the favorable outcomes for T?" Okay? At yung una is determine the sample space of the experiment. Unahin po muna natin yung sample space. So in our sample space, we just need to write down all the possible outcomes. Ah dito we also have here
13:50 head. Okay? Ngayon gagamitin natin yung letters lang para mas maiksi siya isulat. So we have here uh two heads, head and tail, tail and head and two tails. And for our question, for the answer of our question here, what are the favorable outcomes for A? Ano po ba yung event A? A is the event where the coins turn up the same. Okay? Ano po yun? It can only be two heads and two tails. Ito po yung favorable outcomes of event A. Okay, example number two we have here. Suppose a fair coin is tossed and a fair die is ruled. Determine the sample space and the favorable outcomes for the event
14:35 A. The event of tossing a tail and rolling an odd number. Okay. So ano po yung ating experiment dito? It's tossing a fair coin at the same time a fair die. Okay. So, dalawa po no'no. Nag-roll tayo ng die at nag-tos tayo ng coin. Now, determine the sample space and the favorable outcomes for event A. Ano po yung event A? The event of tossing a tail and at the same time rolling an add number. Okay. So, let's now represent the following outcomes. Paano po yun? Here we can use a three diagram. Okay. So, in our three diagram, we can start with the coin. So 'pag nag-tos tayo ng coin, pwedeng dalawa ang possibility. It can be a head or a tail. Next, 'ag
15:23 nag-roll na tayo ng die, ito na 'yung ating ah second experiment. Nag-roll tayo ng die. So, pwedeng madaming possibility. Ilan po ba ang possibility or outcomes if we roll a die? There are actually six. Okay. So, magba-branch out yan from the first outcome in tosing a coin. So, we can have uh the die is 1, two, pwede ring 3, 4, 5, and 6. Next, dito rin po sa ating tail, pwede rin pong mag-branch out iyan into six possible outcomes. Therefore, our outcome, iyung summary natin, we can have the first one is head and then followed by a one dot on the die. Okay. What else? H2. Pwede rin pong H3, H4, H5
16:13 and H6. Next, ito rin po 'ag tail ang nakuha natin sa coin. And then sa die, we have one, we can have T1. Kapag 2 naman po sa die, we can have T2, T3, T4, T5 and T6. Okay, ito po lahat yung mga possible outcomes natin. Okay, to write our final answer, we have here the first one. For the sample space, we have h1 to h yung mga elements natin. And then we have T1 to T6. Okay, ito po lahat iyung outcomes. Next, for the event A, ano yung event A? The event of tossing a tail and rolling an odd number. Okay. So, dito po sa ating outcomes, alin po dito yung event na nag-tos tayo ng tail?
16:59 Of course, dito lang po siya under uh tail. So, we have here T1 to T6. Pero ang hinahanap natin is rolling an add. Okay. So, ano po yung mga add numbers dito? We have 1, 3, and 5. Therefore, our answer is a is equ t1, T3, and T5. Ito po yung ating sagot. Okay, example number three we have here list all possible three digit numbers that can be formed using the digits one 2 and 3 allowing repetition of digits. Then determine the total number of such numbers. Allr so we have here digit 2 and 3. Ano iyung mga possible combinations na pwedeng mangyari from
17:45 this three digits na pwede po yung repetition of digits ha? Madami po yan. So the method that we're going to use now is what we call the systematic listing pa rin. Pero this time we will now be using a table. Pwede po tayong gumawa ng simple table just to organize our outcomes no? Para mas madali nating maintindihan. We can divide the table into three columns. Bakit po? We can have one for the first column, two sa second column, three sa third column. Ito po iyung mga first digits natin at ano po iyung ililista natin? Three digit numbers. Okay? Na gumagamit ng mga numbers na ito. 1, 2, and 3. Allri. We can have for the first column we can
18:31 have lahat ng mga digit three digit numbers na nagsisimula sa one. So we can start with 111. Okay? Followed by 112, followed by 113. Ano pa po? Okay. 1 2 1. Okay. Hindi po tayo gagamit ng four ha kasi nga hanggang 3 lang po yung number natin. So ang papalitan lang natin is yung one sa gitna. So magiging 2 na siya. So 1 2 1. Ano pa po? 1 2 2. Ano pa? 1 2 3. Okay. And we can also have 1 3 1,32 and 133. Okay. So, nauulit-ulit po yung mga numbers 1 to 3 pero magkakaiba
19:17 po yung kanyang arrangement at yung combination. Okay. Next we have here two. Okay. 'Yung first digit niya is two. Ano 'yung unang pwede nating isulat dito? We can have 2 1 1. What else? 21 2 21 2 1 2 221 232 and 233. Okay. Ah meron pa po ba? Wala na. Next for three, first digit is 3. We can start with 31. What else? 312, 313, 321, 322 and 32, 331, 332 and 333. Okay. So, ito po lahat yung mga possible combinations using 1, two, and
20:04 3 numbers. Now, going back to our question, first is i-determine natin ah ilista. So nailista na po natin. Second is i-determine natin iyung total number of such numbers. So ilan po pwede outcomes? All in all, there are 27 possible combinations. Okay. Next. This is a followup question sa ating example number three. Using the same list, let r be the event in which the digits of a threedigit number are not repeated. What are the possible favorable outcomes for R? Ano po yung pwedeng outcome na hindi nauulit-ulit yung mga numbers? Hindi pwedeng ganito, nauulit-ulit yung one.
20:52 Hindi rin pwedeng ganito, 1 2. Naulit pa rin po yung one diyan. So dapat unique lang po yung numbers, no? So yun po yung subset from this sample space. Yun po yung event na kailangan nating isulat. So we can have from the first column magtingin po tayo ng combinations na walang nauulit na number. Okay? We can have the first one is we can have this one 1 2 and 3. Okay? Unique po lahat ng elements diyan. Lahat ng numbers. Ano pa po? We can also have this one. 1 3 and 2. Okay. Next. Wala na po dito sa first column. Sa second column meron po ba? Let's see. We have here 213. Yes. Okay.
21:38 Ano pa po? We also have here 23 1. Okay. And wala na po. Next, sa third column, ano po yung numbers dito na hindi nauulit ang bawat digit? We have 312 and 321. Okay. Meron pa po ba? Okay. Wala na. Therefore, our answer is the elements of event R is 1 2 3 132 213 231 312. Okay? And lastly, 321. So there are how many possible outcomes? 1 2 3 4 5 and 6 possible outcomes for our event are. Okay, example number four. We have here
22:24 a student rolls to fair dieterine all the possible outcomes and identify the favorable outcomes for getting a sum of eight. Okay. So ilang die po ang involved dito? There are two dies. Okay. So let's list down all the possible outcomes. Okay? Ano pong magandang gamitin? Pwede tayong gumamit ng systematic listing. Kasi kapag gagamit po tayo ng three diagram, medyo mas mahirap kasi mas madami tayong space na kakailanganin. But for systematic listing, we can just make use of a table. So ilang columns po ang nandito? We have here six columns. Bakit? Remember in a die there are six possible outcomes. So it can be one, it can be 2, 3 4 5 and 6. Now, under these two
23:12 possible outcomes, since dalawa po yung die na iro-roll natin, yung pangalawang role is pwedeng paiba-iba po ng kanyang ah outcome. So, we can have from the first column, we have pwedeng one. Nasundan ng one sa isa pang die. Pwede rin pong 1 2. Pwede ring 13 and then 14, 15 and 16. Okay. Now, kapag ang first roll naman po natin is two, pwedeng sa susunod na rle masundan po ng one. Pwedeng masundan ng 2, 3, 4, 5, and 6. Ganun din po dito sa 3. We have 31, 32, 33 hanggang 36. Ganun din po pag ang
23:57 first roll natin is four, masusundan yan ng 1 or ah 2, 3 hanggang 6 po sa second role. Ganun din po sa 5 and 6. So ito po lahat iyung mga possible outcomes natin. Next, determine all the possible outcomes and identify the favorable outcomes for getting a sum of eight. Alin po sa ating outcomes ang pag pinag-add natin, ang magiging result niya is 8. So let us identify. Let's go over the following columns. First column, meron po ba dito na pag pinag-add mo yung results nilang dalawa magiging 8? Okay? Wala. Sa second column meron po ba? Okay meron po. Which is 6 and 2. If
24:43 you add this together magiging 8. Okay. Next. Sa third column. Meron po ba? Okay. Yes. Meron po. Which is 3 and 5. If you add them magiging 8. Okay. Sa fourth column mayro'on po ba? Yes. Four and four. Fifth column mayro'n po ba? Yes. It is 5 and three. And then last column meron po ba? Yes, we have 6 and 2. Okay. So lahat po ito, ito po 'yung mga possible outcomes ng ating event. Therefore, our event is equal to pwedeng combination ng 2 and 6. O gagamit po tayo ng parenthesis sa loob ng braces. Ano pa po? 3 and 5. What else? 4 and 4. Next 5 and 3. Next 6 and
25:32 2. So ito po lahat yung mga possible outcomes ng ating event. Okay? Wherein getting a sum of 8. All right. For our last example, we have here the problem. In a certain day, Karindia offers two types of rice. So una, plain rice and yung isang option is garlic rice or yung tinatawag nating sinangag. No, they also serve three types of dish. Yung una is daing na bangus, second is tinola and then sinigang na isda. Ito po iyung mga ulam na ino-offer nila during that day. Now, how many different meal combinations can a customer choose if they pick one ulam and one type of rice? How many includes
26:19 fish? Okay, so dalawang question po ang kailangan nating sagutan. Una is, how many different meal combinations? All in all. And then from those combinations, how many of them includes uh fish? Okay. So paano po natin to isusulat? Paano natin isusulat yung mga outcomes? Anong mas magandang gamitin? Can we make use of table or three diagram? Pwedeng both. But for me, I'm going to use the three diagram. All right? So the first option is rice. Dalawang pagpipilian. It can be P. stands for plain rice and then G stands for garlic rice. Okay. Next, after choosing a rice, we can also
27:04 choose the viand or 'yung ating dish. No by the way, ang vi po ibig sabihin niyan is ulam sa Filipino English. But in standard English, we can use dish. No? Ah pwede pong gumamit ng letter D to represent daing na bangos. Ano pa po? Letter T to represent tinola and letter S to represent sinigang na isda. Okay. Pag pinili naman po natin is garlic rice ganun din po yung options. Pwedeng D, T. Okay. So what are our possible outcomes or iyung meal combinations natin? We can have PD meaning plain rice and daing na bangos. Next we can also have plain rice and tinola. We can also
27:52 have plain rice and sinigang na isda. Kung ang pinili natin is garlic rice, we can have the combinations. GD, garlic rice and daing na bangus. What else? GT, garlic rice and tinola. We can also have garlic rice and sinigang na isda. Okay, so these are all our possible outcomes. Therefore, to answer the first question, how many different meal combinations can a customer choose? We can write our sample space. Ito PDPT PS GD GTN GS. All in all there are six possible combinations. Okay. Now going back to the second question. How many includes fish? So alin po dito sa mga itong outcomes na to ang merong isda? Okay. So
28:38 we have F is equ to PD. Okay. Plain rice with daing na bangus. PS plain rice with sinigang na isda. And then GD garlic rice with daing na bangus and GS garlic rice with sinigang na isda. So ito lang po yung mga possible outcomes natin for our event. Okay? There are how many? Four combinations. Okay. So ito na po. There are six meal combinations and four include fish. Okay. So yun na po lahat ng mga examples natin for determining the outcomes of an experiment. So I hope meron po kayong natutunan sa mga examples natin. Thank
29:25 you very much for listening and I hope to see you again on the next lesson. Okay? God bless po sa inyong pag-aaral. See you again on the next video. Kung meron kang natutunan sa video na ito, please click the subscribe button to support this channel para mas matulungan ulit kita sa mga susunod mo pang matth lessons. Lagi mong tatandaan ang matth ay para sa lahat. At ako si teacher Van. Nagsasabing dito sa math isip lamang ang nag-iisip. God bless and see you on the next video. [Musika]
