00:01
John rolls two dice at the same time.
00:03
He defines the random variable x as the sum of the number showing.
00:07
For example, x can have a value of three in two ways.
00:09
You could roll a one and a two or a two and a one.
00:13
Answer the question below indicating, now i'm not using cells, so i'm just going to answer the questions.
00:22
What are the possible values for x? so the possible values for x are 2, 3, 4, 5, 6, 6.
00:32
7, 8, 9, 10, 11, or 12.
00:37
For part b, we're going to make ourselves a probability distribution table for those values.
00:43
So x and the probability of x.
00:51
And you'll notice this table has some symmetric properties to it.
00:55
So there's one way to get a sum of two.
00:58
There's two ways to get a sum of three, three ways to get a sum of four, and so on.
01:07
Five ways to get a sum of 36.
01:09
Now, seven is our most prevalent.
01:16
There's six ways to do that.
01:17
And then it's going to go down from there.
01:20
So 5 out of 36, 4 out of 36, 3 out of 36, 2 out of 36, and 1 out of 36 ways to get a 12.
01:29
So there's our probability distribution table.
01:32
And from that, i'm going to leave some space for some calculations that will come later.
01:37
So for part c, what is the probability that the sum is four? we could just look at our table and say 3 out of 36, which we could reduce to 1 .12.
01:49
For d, what's the probability the sum is more than 5? again, we could add those values up, 26 out of 36, reduce it.
02:00
We could write our answers in decimal form as well if we wanted to.
02:04
So e, what's the probability the sum of dice rolled is less than 3? again, we can add together the values, although in this case there is only one value, so it's 1 out of 36.
02:17
The probability that x is less than are equal to 5 is 10 out of 36, which would be 5 .18s.
02:28
And the probability that x is greater than 11, again, there's only one way for that to happen...