PROBABILITY

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This video shows the easy method, a general rule to remember the possible outcomes when a coin is tossed, when two coins are tossed and the way to write the two -way table.

Transcript

00:00Today, I am going to discuss with you on a topic, probability.

00:11Here in this video, I will discuss with you event, combined event or compound event and

00:17the two-way table.

00:19This video is by RBA Education and Academy.

00:24I request you to please watch the video from beginning till end.

00:33Now suppose we toss a coin.

00:38So when we toss a coin, what are the possible outcomes?

00:47So see when we toss a coin, there will be only two possible outcomes.

00:54One side of the coin will be head and another side of the coin will be tail.

01:01So either we will get head or we will get tail.

01:06We enclose this in flower bracket.

01:09We call this as sample space, sample space.

01:23So when we toss the coin, what are the possible outcome?

01:27Either you will get head or you will get tail.

01:32Now I want to show you the rule, the rule with which you can easily remember the sample

01:42space whether it is one coin or two coin or three coin, whatever it is.

01:52So in case of tossing a coin, I frame a general rule for you, which I am going to show you

01:58now.

01:59See here.

02:02So this rule says, suppose the number of coins you take as n, then the possible outcome will

02:11be 2 to the power of n, 2 to the power of n.

02:15If you say the number of coin as n, I will do one thing, I will erase this, okay.

02:23Now, okay, if number of coin as n and the outcome as 2.

02:34If number of coin is n, now see here.

02:43So 2 to the power of 1 in place of n, I have taken 1, that is nothing but 2, which you

02:49can see in the table, 2 to the power of 1 is 2.

02:52So there will be two outcomes.

02:54Just we have seen that is head and tail, one is head, one is tail.

03:02If there are two coins in place of n, keep it 2.

03:08This is only in case of coin, this you cannot generalize with other things.

03:12I am saying in case of coins.

03:15So you can take the total possible outcome as 2 to the power of n.

03:19So 2 to the power of 2, that is 2 times 2, 2 multiplied by itself, we get 4.

03:27So there will be four possible outcomes we will discuss now.

03:31Now suppose the coins are 3 or you flip the coin 3 times, okay, you toss a coin 2 times

03:37or two different coins are tossed.

03:40So in case of two coins, 2 to the power of 2, in place of n, since the coins are 2, 2

03:45to the power of 2, 2 times 2, 4, suppose there are three coins.

03:49So in place of n, 2 to the power of 3.

03:53Now here I write 2 times 2 times 2, 2 times 2, 4, 4 times 2, 8, there will be 8 possible

04:03outcomes.

04:04So once again, when one coin is tossed in place of n, 2 power of n, 2, there will be

04:11two outcomes, head and tail.

04:14When there are two coins in place of n, 2, 2 to the power of 2, 2 times 2, you can see

04:20in the table, that's 4, there are four outcomes.

04:23If coins are 3, n equal to 3, 2 to the power of 3, 2 times 2, 4, 4 times 2, 8.

04:30So there are 8 possible outcomes.

04:34So now boys, see here, very easily, you can keep in mind, okay, when one coin is tossed,

04:46you will get either head or tail.

04:50You can get head or you can get tail.

04:54So the sample space is head and tail, head comma tail.

04:59Now suppose, now we are going to discuss compound events or combined events.

05:08Here in combined events, we discuss two or more events.

05:15When two coins are tossed, write the sample space diagram, or you can also call it as

05:26possibility space diagram.

05:28First, compound events look at the probability of two or more events.

05:35What I'm saying, it look at the possibility of two or, or more events.

05:54Now boys, suppose here we are taking two coins.

06:03So I will write coin number 1, okay, and coin number 2.

06:13Now if I take head, if I throw one coin, two coins, suppose on one coin, I get head, on

06:20second coin also I can get head.

06:22There is chance that, possibility that I will get head on both the coins.

06:28There's also possibility that on first coin I get head, on second coin I get tail.

06:35There's also possibility that I get tail on first coin and head on second coin.

06:41And the last possibility is that we get tail on both the coins.

06:46So when n number of coins, n means here, not n.

06:50When the coins are 2, n is equal to 2, what are the total possible outcomes?

06:552 power of n, that is 2 to the power of 2, 2 multiplied with 2, that is 4.

07:04I told you n means number of coins, number of coins is 2.

07:08What are the total possible outcomes?

07:092 to the power of n, 2 power of 2, 2 times 2, 2 multiplied by itself, that is 4.

07:16You can see the four possible outcomes.

07:19Case number one, head on both coins.

07:22It is possible that we get head on first coin and head on second coin.

07:25It is also possible that we get a head on first coin and we get tail on the second coin.

07:31This is our second possibility.

07:33And third possibility, tail on first coin and head on second coin.

07:38And the last fourth possibility, tail on both the coins.

07:42So this, the sample space now that is formed, we write this in ordered pair and impose in

07:55flower brackets.

07:57So the sample space, okay, here the sample space is, we can write as head, comma, head

08:11on both the coins, head on first coin, tail on second coin, tail on first coin, head on

08:19second coin and tail on both the coins.

08:23So this is the sample space when two coins are tossed.

08:29So remember boys, the general rule, make it very easy for you to remember the sample space

08:36and what are the possibilities.

08:39So whenever you get in examination, remember n and 2 to the power of n.

08:44Once again, coin one and coin two, head on first coin, head on second coin, head on coin

08:52number one, head on coin number two.

08:55This is first possibility.

08:56And the second possibility, head on first coin, tail on second coin.

09:02The third possibility, tail on first coin, head on second coin.

09:08And the last possibility is head on both the, tail on both the coins.

09:14So the sample space that is formed is head, comma, head, head, tail, tail, head and tail,

09:21tail.

09:22Now boys, last we will discuss the two way table showing the possible outcomes.

09:30So here, we take coin number one, coin number two, we do like this.

09:39Then after that boys, okay, if we draw a table like this, okay, we will divide into rows

09:53and column.

09:54Now, here I will take head of first coin, let's wait a little bit, come on, head on

10:08first coin and tail of first coin, I will draw one more line, head of second coin and

10:18tail of second coin, head I represent by H.

10:23So when I throw the two coins, it's possible that I get head on first coin and head on

10:29second coin.

10:30So this, okay, this represent head and head.

10:34Then head of second coin, tail of first coin.

10:37So I can take H, T, head of second coin, tail of first coin, the tail of first coin and

10:44head of second coin, tail H, neither we can take or tail of second coin and tail of first

10:51coin, tail, tail.

10:53So like this, the sample space is again head, head, head, tail, tail, head and tail, tail.

11:10So this is the way to represent the two-way table.

11:15So, now boys, so that you can remember it very easily.

11:27Head, now see here, head of first coin, okay, I will do one thing, head of first coin, tail

11:42of first coin and here head of second coin, tail of second coin.

11:51Then we throw the two coins, head of second coin and head of first coin, we get this outcome.

11:59Then the second possible outcome, head of second coin and tail of first coin, head and

12:03tail, tail of second coin and head of first coin, tail H, then tail of second coin and

12:09tail of first coin, T, T.

12:11So the sample space is head, head, head, tail, tail, head and tail, tail.

12:21I hope you understand the video.

12:23Thanks for watching the video.

12:25This video was by RBA Educational Academy.

12:29Please like, share and subscribe.

12:34We'll meet again.

12:35Till then, bye bye.

12:36I love you.

12:37Please like, share and subscribe.

12:39Once again, the course for me.

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