00:01
So we know that the best of four, so four out of possibly seven games we have for like a world series.
00:10
And if we have the probability that a wins over team b is 0 .52, we want to know in the first question, what is the probability that a wins in six games? well, that means in the first five games that we have to have a needs to win three.
00:33
And we don't know where those three are, but it could be winning any of those three.
00:37
And then the sixth game, a, has to win.
00:41
So this first part is binomial.
00:44
And so we have that combination of five games, choose three times a winning.
00:51
And we want a to win three.
00:52
And that means we want b will win two of those five.
00:57
And then we have a winning the sixth game, which is 0 .52.
01:02
And so this five choose three is five times four divided by two.
01:09
So this is ten.
01:11
So if we take ten times point five two, it's going to end up being to the fourth power, to the fourth power, times point four eight to the second power.
01:24
And let me quick messed up.
01:28
I'm putting a couple things in the calculator.
01:30
There we go.
01:33
Times 0 .48 to the second power.
01:38
And that comes out to be a probability that you went in 6 of 0 .168, and it would round to 5.
01:46
So about a 17 % chance.
01:48
And i'm just going to store that value as alpha a in case i need that again, which i think i do.
01:53
So we're going to store that as alpha a.
01:58
And i'm just going to put a sub's little indication there.
02:01
Now, the second question asks, what is the probability that a wins? well, a could win in four, could win in five, could win in six game, or could win in seven.
02:16
We already know this answer.
02:19
If winning in four means that we would have this happening in four times.
02:24
In five would mean that in the first four games, in the first four games, a wins three of them.
02:35
And b11.
02:38
0 .4 .8 to the first...