00:01
So with this question, they say that a fair guy is rolled twice.
00:06
We're going to let a denote the event that the sum of the outcomes is odd.
00:13
And we're going to let b denote the event that it lands on two on the first toss.
00:21
We want to calculate the probability of a and the probability of a given b.
00:30
Are a and b independent.
00:35
Okay, so first, let's say we're rolling a dye twice.
00:40
What do we know? we know that the possibilities are 1 -1, 1 -2, 1 -3, 1 -4, 1 -4, 1 -5, 1 -6, followed by 2 -1, 2 -2, 2 -2, 2 3, 2 4, 2 -2, 2 -5, 2 -2, 2 -6, 2 -4, 2 -4, 2 -5, 2 -2, 2 -6, 2 -6.
01:04
And then we're going to have 3 -1, 3 -2, 3 -3, 3 -4, 35, 36, followed by 4 -1, 4 -2, 4 -3, 4 -4, 4 -5, 4 -6.
01:33
After that we have 5 -1, 52, 53, 5 4, 4, 4, 4, 4, 4.
01:43
5, 5, 6, 61, 62, 63, 64, 65, 66.
02:01
And so there are 36 different possibilities here.
02:05
Now first, if i want the probability of a, a is the event that the sum of the outcomes is odd.
02:12
Well, let's see where that occurs.
02:15
These guys add up to three, so those two.
02:20
And then these guys add up to five, so these four.
02:29
And then these guys here add up to seven...