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PROFESSOR: So you've already seen a little bit of the story of forward mode and reverse mode from Stephen last week. One version of the story is that you're multiplying derivatives, or Jacobian matrices, or something like that. And, of course, you've heard Stephen say that matrix multiplication is associative, and so you can go left to right or right to left, but it matters what order you go in terms of the complexity of the computation. That one order might be an n cubed computation, and another order might be an n squared computation. And so you saw an example of that. And in some fundamental sense, that describes the entire story of forward and reverse mode. But in a way, I feel like it hides more than it reveals. And the story is-- in some sense, the entire story can be reduced to that. But I feel like that's not enough to fully understand. And so I put together this example that I used in my class last semester. And I'm just going to pull it all o...

You've tested positive for a rare and deadly cancer that afflicts 1 out of 1000 people, based on a test that is 99% accurate. What are the chances that you actually have the cancer? By the end of this video, you'll be able to answer this question! This video is part of the Probability and Statistics video series. Many natural and social phenomena are probabilistic in nature. Engineers, scientists, and policymakers often use probability to model and predict system behavior. Hi, my name is Sam Watson, and I'm a graduate student in mathematics at MIT. Before watching this video, you should be familiar with basic probability vocabulary and the definition of conditional probability. After watching this video, you'll be able to: Calculate the conditional probability of a given event using tables and trees; and Understand how conditional probability can be used to interpret medical diagnoses. Suppose that in front of you are two bowls, labeled A and B. Each bowl ...