00:01
So we have to pay $5 to play and we are rolling two dice that are fair.
00:16
So our possible outcomes for each roll, well you can either roll two once, which is a two.
00:43
You can roll a three, you can roll a four, you can roll a five, you can roll a six, all the way up to twelve when you roll two sixes.
00:57
And then the probability, so let's see here, two is going to be one plus one, so that only happens once.
01:09
Then three can be a one plus a two or a two plus a one, so that has two.
01:17
Four can be two plus two, or it can be a one plus a three or a three plus a one, so that has a frequency of three.
01:36
A five can be a one plus a four or a four plus a one or a two plus a three or a three plus a two, so that has four possible ways of rolling a five.
01:55
Six can be a one plus five, five plus one, three plus three, two plus four, or four plus two, so that has five ways of rolling that.
02:08
A seven can be a one plus a six or a six plus a one or a two plus a five or a five plus a two or a three plus a four or a four plus a three, so that has six ways of rolling it.
02:26
Eight can be a two plus a six or a six plus a two or a three plus a five or a five plus a three or a four plus a four, so that is five ways of rolling an eight.
02:43
Then a nine can be a three plus a six or a six plus a three or a four plus a five or a five plus a four, so that is four ways.
02:57
A ten can be a four plus a six or a six plus a four or a five plus a five, so there's three ways of rolling a ten.
03:07
Eleven can be a five plus a six or a six plus a five, so there's two ways of rolling that, and twelve is just a six plus a six, one way of rolling that.
03:19
So the total number of ways that we can roll the die is going to be one plus two plus three plus four plus five plus six plus five plus four plus three plus two plus one, thirty -six.
03:41
And then, let's see here, if we roll a two, the net or the house pays, let's see here, if you roll a two, a three, or a twelve, the house pays fourteen.
04:05
If you roll a six or an eight, you get ten dollars from the house, so that's a six or an eight...