Solved – a good example to illustrate the distinction between objective and subjective probability

As I understand it, objective probability is based on a frequency of something occurring over an infinite number of observations. A typical example would be: "the probability of getting heads is 50% because if I flipped a coin often enough, I would get heads 50% of the time".

Subjective probability is your belief in the probability of a single event. An example might be: "the probability of it raining tomorrow is 40%; this is just speaking about a single observation, as you can't repeat the day over and over".

Is my understanding correct? Are these two examples correct?

The example I always use comes from Ted Dunning (at least, he was the first person I can attribute this to). Typically it's performed live with a real coin and $ N ge 2$ people.

I have a coin in my hand, and I flip it without revealing it. I ask person 1 what's the probability of heads. They respond 50%. I then show person 2 the result of the flip, without person 1 seeing, and ask what's the probability of heads to person 2. The respond either 100% or 0%. Thus, we have two individuals giving very different probabilities about the same event. Thus probability is subjective.

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