00:01
So in this question, we are asked to find the size and only the size of the sample space for the following situations.
00:06
And the information we're going to need in order for us to be able to answer this is just our multiplication rule of counting, right? we're going to need to understand that inside out.
00:15
And the way we're going to explain it is like this.
00:18
If we're dealing with two independent events, right, so two events that don't really have any impact on each other, right? and we can think of it like this.
00:28
Like an example could be like you flipping a coin and you're rolling a die, you know? whatever you flip on the coin isn't going to affect what you roll on the die, right? okay.
00:39
So following that knowledge, if we're dealing with two independent events like we've described above, if there are a ways to do the first thing, and there are b ways to do the other thing, and they're both independent events, and the number of ways we can do both things is equal to a times b.
00:53
Okay? so now that we know that, we can apply it to our question.
00:59
Okay? so let's start off with part a.
01:02
We're telling us that we're rolling a pair of 20 -sided dice, right? so we know that for each of our dice, we're going to have 20 outcomes that we can get.
01:11
Okay? so if we have dice 1, we have 20 outcomes.
01:15
And if we have dice 2, we also have 20 outcomes here.
01:18
Obviously, what we roll on the first dice isn't going to, like, affect what we roll on the second one, right? so it means that these are independent events.
01:26
And so we can find the total number of ways we can roll these.
01:29
These dice by multiplying them together.
01:32
And so we know 20 times 20 is equals of 400.
01:36
So that's going to be our answer for part a.
01:40
Now for part b, we're told that we're rolling a 20 -sided dice and then we're flipping a coin.
01:46
So obviously, logically, it doesn't matter what we roll on our dice, and then when we flip a coin, so it's not going to have any impact, right? whichever when we do first is not going to have an impact on the other.
01:59
And so because of this, if we're going to go back to our multiplication rule of counting, we know that if we are going to roll our dice, we have 20 ways we can do that.
02:08
And if we're going to flip our coin, there are two ways we can do that, right? so following our multiplication rule of counting, 20 times 2 is equal to 40, and that's going to be our answer for part d.
02:19
Sorry for part b.
02:21
Okay.
02:21
Now, for part c, we are told that we're flipping 12 coins, and then we're rolling a 10 -sided dice, right? so what we're trying to look for here is the number of ways we can flip 12 coins, and then we're going to be multiplying that by the number of ways we can roll our 10 -sided dice, which you already know is going to be 10.
02:40
Okay? so if you're going to try and find our outcomes flipping our 12 coins, we can actually look at this as another application or another use of our multiplication rule of counting.
02:50
We know that we have 12 coins, right? and for each of those coins, there are two things we can choose.
02:57
So 12 times 2 is going to be equal.
03:02
To 24.
03:04
Okay? so we're going to have 24 times 10, which is going to be 240, and this is going to be our answer, steve...