00:01
And this question is given that there are 18 balls number 1 through 18 in a box.
00:07
Two balls are drawn in succession and without replacement.
00:13
I'm going to let a denote the event the first ball drawn has a smaller number than the second ball.
00:18
And b denote the event that the second ball drawn has the number four on it.
00:23
Now we want to find probability the first ball has a smaller number given the second ball had the number four on it.
00:31
So we want to find probability.
00:35
The first ball had a smaller number.
00:37
That's event a given.
00:39
Now given is this vertical line here.
00:41
The second ball had number four on it.
00:44
That's event b.
00:46
Now this is conditional probability.
00:49
We want to find probability of event a given that event b has already occurred.
00:54
Using the bayer's theorem, the formula would be probability of a intercept b over probability of b.
01:04
Now intersect means n and is multiplication, all means union and is plus.
01:17
So a intercept b means a and b.
01:20
Both events occur at the same time.
01:23
That is, the first ball has a smaller number than the second ball, and the second ball's number is four.
01:32
So this will be a few mutually exclusive event.
01:37
The first event will be the first ball has the number one and the second number on the ball, second ball is four.
01:50
Now all is plus.
01:53
The first ball has the number two and the second ball has the number four.
02:00
Or the first ball has the number three and the second ball has the number four.
02:10
So you can see that the first ball's number is less than the second.
02:15
Now we divide by probability of b, that's probability the second ball has the number four.
02:23
Now we do not care whether what the first ball's number is, as long as the second ball is the number four.
02:34
So that would be the first ball can be any number except the number four.
02:39
So we know that there are 18 balls in the first round.
02:44
There will be 17 balls that does not have the number four.
02:48
So it would be probability the first ball does not have the number four will be 17 out of 18...