00:01
So in this question, we're told that we're given two distinguishable and fair four -sided dice.
00:05
Okay? we're supposed to find the probability that the sum of these dice values is at least five.
00:11
We're supposed to leave our answer as a fraction, and we're not supposed to compute a rounded decimal.
00:15
So, in order for us to figure this out, let's first look at our sample space.
00:21
Okay? we know that we have two dice.
00:24
Since they're distinguishable, we can do one in red and one in blue.
00:27
We know that for each of these dice, we have four possible options.
00:30
We can roll for them, right? you can roll a 1, 2, 3, 4 for the first one, and then a 1, 2, 3, or 4 for the second one.
00:40
Okay? and we know that since these are distinguishable, these probabilities are the chance, like the number of ways we can roll all of our dices, they're going to be independent of each other, right? and so, with that mind, i just want to bring up our multiplication rule of counting, which states that if we have a ways to do one thing and b ways to do another thing, then the number of ways we can do.
01:02
Do a and b things, like both of them, is a times b.
01:06
Okay? so also means that in this case, if we have like a ways to roll the dice the first time and b ways to do it the second time, then if you multiply these together, we can get the number of ways we can roll our dice together, right? so obviously we have four options for each of these dice.
01:25
So we're going to have four times four, which is 16.
01:28
Okay? so there are 16 total ways to roll the dice.
01:35
But i think in this case is also going to be helpful for us to look at our sample space in the respective sums, right? so i'll just do it in white.
01:47
So you know that if we're just going to go like this, so when we roll one the first time, then we can roll any one of these the second time.
01:56
If you roll a two the first time, then we can roll any one of these the second time.
02:02
Okay? so if we're going to follow that knowledge, what we're going to have is 1 -1, 1 -2, 1 -3, one four, one five, sorry, two, one, two, two, two, three, and two, four.
02:38
Then if you're going to continue, we know we have three one, three two, three three, and three four...