00:01
All right, in this problem we have a definition of odds and odds is the ratio of the probability of an outcome over the probability of that outcome not occurring.
00:09
So let's think about how we normally hear odds, right? let's just say like you go to the horse races, right? and you're saying that you're going to bet on horse one because the odds are 10 to 1, right? so they would say that it's 10 to 1.
00:23
Now what that means, or you might write it as 10 to 1 with like that, or you might write it 10 over 1.
00:31
Now when we hear that, when we say 10 to 1, we're saying there's 10 ways for them to lose, right? the probability of them winning is 10 out of 11.
00:42
And the problem, so this is the probability of winning, right? so this is how we would say, or actually it would be the probability of them losing.
00:48
So the probability of them losing, right, is going to be 10 out of 11.
00:54
And then we'd have the probability of them winning is 1 out of 11, 1 out of 11.
01:02
And that's why we say it's 10 to 1, right? so there's 10 ways to lose and there's one way to win.
01:08
So what we're saying is, is that it's 10 over 11.
01:11
So we would say 10 over 11 over 1 out of 11, 1 out of 11.
01:17
And that of course, as an improper fraction or as a complex fraction, we can write that as 10 over 11 times 11 over 1, which is going to be 10 to 1.
01:27
All right...