00:01
So we're told in a state lottery we can bet $4 by selecting three digits, each between 0 and 9.
00:12
And if those numbers we pick are drawn in the same order, we win and collect $700.
00:21
Let me get rid of these extra zeros on the $4 for the cents.
00:25
We're going to have to do all cents right now.
00:28
And we're going to do some analysis with this.
00:30
So the first thing we do is what's the probability of winning? so the probability of winning.
00:36
Well, let's think about this.
00:37
If we have three numbers, 0 through 9, 1, 2, 3, right? three numbers, number 1, number 2, number 3.
00:44
There's a total of 10 numbers for each.
00:47
So 10 times 10 times 10 is 1 ,000.
00:49
And it's 1 out of those 1 ,000, 1 out of 1 ,000.
00:52
So the probability is 1 ,000.
00:57
Now, we want to know, if we win, what's our net profit? so if we win, what's our net profit? well, we bet $4 and we got $700, so that means the net profit is our earnings, $700, minus what we paid for it, so $696.
01:22
Now we're going to find the expected value for this $4 bet, and that's what this thing's floating out here, this x, 700, negative 4.
01:28
So this is the winnings...