Conditional Probability

Now let me ask you a really tricky question. What is the probability of a positive test result? Can you sum or determine, irrespective of whether there’s cancer or not, what is the probability you get a positive test result?

And as usual, the answer is 1. That is, we study in the truth table all possible cases. and when we add up the probabilities, you should always get the answer of 1.

Now quickly, do me a favor and add all of those up. What do you get?

Here you get 0.72, which is the product of not having cancer in the first place 0.9 and the probability of getting a negative test result under the condition of not having cancer.

Let’s just quickly do the final one, because it’s the most likely one.

And here the answer is 0.18 by multiplying the probability of not having cancer, which is 0.9, with the probability of getting a positive test result for a non-cancer patient 0.2. Multiplying 0.9 with 0.2 gives me 0.18.

Moving on to the next case. What do you think the answer is?

In real life, events often depend on each other. Say you can be an early bird or night owl. And for the sake of simplicity, let’s assume there’s a 50 percent chance for each one. Now whether you decide to go for a run at 5:00 a.m. tomorrow is not entirely independent. I would argue … Read more