00:03
Okay, we're told to roll two dice and find the probability that the minimum of the two numbers is greater than four.
00:10
I'm actually going to go through this two separate problems.
00:13
I'm not 100 % sure if they mean the minimum of those two values themselves.
00:18
Like if you roll a five and a six, you know, what's the probability the minimum of either of those two numbers is greater than four? but often they're talking about the sum.
00:28
What's the probability the minimum sum of the two numbers is greater than four? so let's kind of look at both of those and then you can decide which one is actually being asked for here.
00:37
I think the easiest way to answer any of those questions is go ahead and think about your sample space.
00:42
When you roll two dice, you might get a one followed by a one or a one followed by a two, one followed by a three, one four, one five, or one six.
00:51
But you might start with a two, two, two, two, three, two, four, two five, and two six.
00:58
This is a little annoying.
00:59
You don't want to do this all the time, but certainly it doesn't take too long to write all of your possible combinations out.
01:07
And then it really makes things a lot easier as we're talking about these different probabilities.
01:12
4 -1, 4 -2, 4 -3, 4 -4, 4, 4, 4, 6, 4, 4, 6, 5, 5, 2, 5, 5, 5, and 5, 6, 6.
01:24
And then 6 -1, 6 -2, 6, 6, 4, 6, 5, and 6 -6.
01:30
This is the sample space of all 36 things that can happen, 36 different combinations that can come up when you roll two dice.
01:39
Now, what is the probability? the minimum is greater than 4.
01:43
So we know that our probability is going to be out of 36 because there's 36 samples here.
01:49
All right.
01:50
So what would the, if they want just the minimum of, either of the numbers to be greater than four, that means we can only get fives and sixes, the minimum of them.
02:03
So the smaller of them can only be a five or a six.
02:07
So if that is the true probability, then we only have these four combinations where the minimum, right, the smaller of the two numbers is greater than four.
02:16
Okay...