Jerry Roth thanks for reading. Great question! Questions like yours help me improve as a data science writer, so I appreciate you commenting.

So, conditional probability doesn’t tell us that if Event B happens then Event A will probably happen. It tells us the probability of Event A happening IF we know that Event B happened for sure. That probability could still be very small.

Using your example above, if we know that someone is HIV positive (Event B), conditional probability can help us calculate the chances that the person will get AIDS (Event A). This is actually an excellent example. Thank you for bringing it up.

With new treatments available on the market, the conditional probability P(person develops AIDS | person is HIV positive) has actually decreased.

I hope that helps.

Also, James Finn is a writer on this platform, and he has written extensively about HIV, AIDS, and treatment. He’s a great writer to check out if you enjoy analytical insight with heart.