Probability?

The frame of the plane shudders and I think to myself, “The plane’s gonna crash.” Contrary to what you might expect, saying this calmed me down. Why? Here was my reasoning – “OK, so me thinking that the plane will crash makes it less likely that the plane will crash because:

1) if it was already unlikely that the plan would crash

2) and I predict that the plane will crash

3) what are the chances that I predict an unlikely event happening and it happens (e.g., what are the chances that I predict the lottery winning ticket)?
4) Very low, right?

 

Of course, in the real world, this thinking is not correct because the chance of the plane crashing doesn’t depend at all on my thoughts. Nonetheless, this reasoning was comforting despite the faulty probability calculations.

 

But how does probability actually work? I want to tackle this question in this blog.

 

The upcoming ideas about probability are wholly inspired by Feynman’s Lecture of Physics. I highly suggest you check out his lecture on probability.

 

What are probabilities? They are guesses we make about the world. If we say a coin has a 50% probability of flipping heads, this is just a guess. We may flip a hundred tails in a row, never flipping heads. Does this mean that our probability was wrong? No. Probabilities are only educated guesses we make about the world. The real world need not follow them, though we predict that this is unlikely.

 

We make this educated guess based on the result we think is most likely. Of course, we may flip a hundred tails in a row. But, when we say that the probability of flipping heads with a fair coin is 50%, we guess that the most likely outcome is that upon flipping 100 coins, 50 will be heads, and 50 will be tails. It’s just a guess (based on rigorous reasoning).

The mathematics of probabilities is a system to make these guesses better.

 

This is the essence of probability. Here is how Feynman defines it in his Lectures on Physics:

By the probability of a particular outcome of an observation, we mean our estimate for the most likely fraction of a number of repeated observations that will yield that particular outcome.

 

This definition is very enlightening. It follows that we can never have absolute knowledge whenever probabilities are involved. 

 

Again, I highly suggest checking Feynman’s Lecture on Probability out to learn more.