Question

It makes sense to talk about the probability of a series of coin tosses but what about seeing a TV on a wall, or seeing a person riding a bicycle on the street?

If one were to compare an event such as a person riding a bicycle on the street vs. a coin landing on heads 10,000 straight times, the second very strongly and intuitively seems more improbable.

But is it, or is it just that the probability of the other event isn’t as well defined? If it isn’t well defined, how does one compare the "likelihood" or "ease" at which nature can produce an event like 10,000 heads vs. a person riding a bicycle?

The second issue I seem to have trouble grasping with is depending on how I describe the event of a person riding a bicycle, the hypothetical probability of it seems to be different. John riding a bicycle vs. John riding a bicycle at 7 PM vs. John riding a bicycle at 7 PM on MacArthur street seem to be events with decreasing "probabilities".

Specifying details of an event seems to be adding evidence, not subtracting it away. Thus, the more specifically detailed the event is, the more evidence one includes about the event. But this suggests that the "actual" probability of the event is when it is defined with as many specific details as possible. But this also makes the event seem to have a very low probability. What is wrong or right about this, and how can one compare the "rarity" of an event like this with a series of coin tosses?

Answer 1

In probability, coin tosses possess a well-defined chance of occurrence, exemplified by the law of large numbers; however, the likelihood of complex events, like a specific person riding a bicycle, becomes less clear as it incorporates numerous variables making it less intuitively comparable to simple events.

Step-by-step explanation:

Understanding the probability of complex events versus simple events such as coin tosses can be challenging. The probability of a coin landing on heads is well-defined at 0.5, thanks to theoretical probability and confirmed by experimental results, like those of Karl Pearson and others, demonstrating the law of large numbers. However, when it comes to more detailed and complex events, such as John riding a bicycle at a certain time and place, the mathematics of probability becomes less intuitive. The hypothetical probability seems to change when we add more details because we are analyzing a different, more specific event each time. Therefore, as we add more details, the probability of the event occurring exactly as specified may appear lower, yet that's simply because we are looking at a narrower occurrence within the broader possible outcomes.

Comparing the rarity of a series of coin tosses resulting in 10,000 straight heads to the nuanced probability of a detailed event such as someone riding a bike requires understanding that the two are qualitatively different. Coin tosses have a clear and quantifiable probability, while the nuances of a complex event require consideration of so many variables that they might not be well-defined probabilistically without detailed context and data.