00:01
All right, so we want to calculate the expected probability, the expected value of this game, where you're going to roll a diet three times.
00:09
So there's six possible outcomes for the first time, six for the second and six for the third.
00:16
So that's six to the third power, which is going to be 216 possible outcomes.
00:25
And you're going to lose $20 if you get at least one, two.
00:37
Otherwise you're going to win $7.
00:41
So let's determine the number of times that you'd get at least one, two.
00:48
So basically we can do it over here.
00:50
So for the first roll, you could have a one, a two, a three, a four, a five, or a six.
00:57
And then for each of these, there's going to be 36 possible outcomes, six for the second rule and six for the third row.
01:07
So for all of them that have this two for the first roll, you're going to have at least one two.
01:14
So that's 36.
01:15
So i'll put it in a circle here.
01:16
And then i'm going to add up all the numbers in a circle.
01:18
Now, for any other situation, if you get like a number on the first roll, that's not a two, then you would get a two on the second roll.
01:26
And then for each of the six numbers on the third roll, that still count.
01:31
So that's six...