00:01
Okay, so here we're looking at some probabilities and we have two dice.
00:05
So the first part is just we're letting our variable y be the sum of the dice.
00:14
And so we want to know what are the possible answers.
00:16
Well, the minimum would be if we rolled the smallest value of each dice, which is one.
00:21
So that's going to be a two.
00:25
And then we can have basically every combination up to the highest, which would be if we had two sixes, which is going to be a 12.
00:32
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 is going to be the possible values for the sum.
00:49
Okay, and so then part b wants us to use random variable notation to represent the event.
00:54
This varies a little bit, which is annoying.
00:58
But the main thing is that it goes inside brackets.
01:00
So usually an event gets shown as being, say, like, y is equal to 7.
01:07
I say it varies because some folks might use the non -curly brackets, but the idea is that it goes in brackets.
01:13
And then when we start trying to say something about the event, we might put like a p out here, like the probability of the event occurs.
01:21
Or you might add something else to the brackets showing you you're calculating something about that event.
01:29
Okay, so c wants us to think about, well, what is the probability that y is equal to 7? so if we think about our dice, we have each one goes from one to six.
01:50
So how many ways can we get seven? well, i could roll a one and a six, two and five, three and four, four and three, five and a two, or a six and a one.
02:06
Okay, so that was six ways that we can get seven, and that is out of the total of 36 different combinations we can get when we roll two dice.
02:17
Okay, so 6 out of 36 or 1 .6 is going to be the probability that our two roles add up to 7.
02:32
So now we're looking at part d, and part d says to find the probability distribution of y.
02:47
Okay, so if we have our values 2 through 12, where is the probability basically of getting each one? so we know that the probability for getting a 7 is 6 out of 36.
03:03
Okay, what is the probability that we'll roll a 2? well, we'd have to get a 1 in a 1 on our dice.
03:08
There's only one way to do that, so that's going to be 1 out of 36.
03:13
What's the probability of getting a 3? we could roll a 1 and a 2 or a 2 and a 1.
03:18
So that's going to be 2 out of 36.
03:23
Okay, the probability of getting a 4, we could roll 1 and a 3, a 3 in a 1, or a 2 and a 2.
03:29
That's going to give us three out of 36.
03:33
So then we go to five...