00:01
Hi, i'm david and i'm hitchie.
00:02
Help you answer your question.
00:03
Now let me bring up your question here.
00:06
In the question here, alas and pop begin to play a sequence of chess games and s stands for alas win the game.
00:16
And suppose that outcomes of successing games are independent with the probability that s equal to the 7 .6.
00:23
They will play until one of them wins two games in a row.
00:27
And if this does not happen then the winners is the one who wins the most out of the five games so let's try to write down the sample space now so if s will be the outcome that a less wins the game and then i will let the be that be we now buffed in the game so therefore we will have the chance that alice will win at the same, the two games and the row will be the ss.
01:16
And it can also that the bob will can win the two first games in the row.
01:22
And that will be the case where we have only the two games happens.
01:26
And the second case, it can be the case that there will be the three games.
01:31
So it will be something like the bob win first and then alice win two games in the row.
01:36
Or the alex win at them, bob wins two games in the row.
01:42
That will be the case that there are only the two games.
01:46
The next one, there will be the three, there will be the four games, where we will have the case that will be the alice win first, and then bob wins and then alex.
02:01
And it can be the case that will be the bob will be.
02:09
First and then a last win after and then pop win and pop wins and then it will have the sbps and then bbsp so i think that will be the only case we will have here and that's the last one will be when we have the five games at the same time and then we will have the case that will be the sbsbs and then it can be the sbs and it can be the sbs and it can be the bs and it can be the bs and it can also be the case that will be the sbs and then it can also be the case that will be the sbs and it can also be the case that will be the sbs and it can also be the case that will be and then we have the pop -up at the same times, and then the psb, and then we have the s and s.
03:26
So that will be the total sample space we can have such that that will win two games in a row, or that they will play the five games.
03:37
And now we want to write down the bmf on the x, where the x will be the number of the games played.
03:43
So therefore we will have the x here, it will have the value where we can say this one will be the x can take the value under two games, three games, four games, and the five games.
04:08
And this will be the probability of the x.
04:10
Now we see in the two have the two games and then we have only the two cases here and we will have s s means that we have the 0 .6 that alice will not the same.
04:22
Time and then power 2.
04:24
And the second case will be pops win at the same time will be the 0 .4 because pops win will be the 0 .0 probability to the p equal to the 1 minus 0 .6 equal to the 0 .4.
04:34
And then we have the power 2...