This lesson will introduce experimental and subjective definitions of probability.
This tutorial will discuss the relative frequency probability method by discussing specifically:
It's important to know that relative frequency probability method is relatively based on past experience.
Here is a chart for coin flips. You start where it says start. If you flip heads-- for this scenario heads will be defined as being a win-- you will go to go up the line, meaning, the blue line that draws up to 100%. If you flip heads on the first trial, your experimental probability is 100%. If you flip heads on the next trial, it remains 100%. If you flip a tail, then it reduces all the way down to 66.6%, etc.
And if you flip tails, you're going to go down the next line to the next dot. This is showing is experimental probability of heads. You can keep flipping coins to see what happens.
The next one was heads, the next one was tails.
And you can simulate, sort of, the rest of what happens with continuous flipping of coins.
What do you notice? The graph is pretty erratic at the beginning, but it begins to settle down towards the end. And where does it settle in? Right around 50%.
The longer you run the experiment, the closer the blue line would stay to this red line. If you kept going forever, the blue and red would be indistinguishable.
The most frequent approach-- it's also called the relative frequency approach-- says that the probability of an event is the number of times it's occurred in identical trials, divided by the total number of trials.
The relative frequency probability model is also called the empirical method or experimental probability?
In the case of the coin flips, the chart indicates the probability of a coin coming up heads is 50%, not because there are two faces to the coin, but rather because heads has come up about half the time in repeated trials of coin flipping.
One additional way to talk about probability is called the subjective probability approach. It's not a mathematical model like some of the others that we talked about, like the frequentest approach or the a priori model, but it's based on your judgment, your overall how you feel about something.
And you hear words like this all the time.
"I'm 90% certain I left the garage open".
Does that mean that if the frequentest approach was used, you would say "90% of the times that I felt this way I did in fact leave the garage open?
It just doesn't really make a lot of sense. You would basically be saying that you're more sure than not sure that you left the garage open.
"I'd say there's about a 50-50 chance I got the job."
Again, what does that mean? About half the time you felt this way you ended up getting the job? This isn't a frequentest approach. This isn't any mathematical model.
"There's a one in a million chance of surviving that kind of accident."
Again, they're just saying that they don't think that that's very possible or very probable. They're not saying that there's been a million such accidents and only one person survived.
The relative frequency model is the one that we're going to mainly use. And it deals with looking at the past to see, relative to the total number of experiments that I've done, how many of them came up with this particular event. So, the relative frequency is defined as the probability of the event. We also talked about subjective probability and how that's not really a probability, technically. But it's more how you feel about it. and we're going to leave that more to psychology to talk about.
Good luck!
Source: This work is adapted from Sophia author jonathan osters.
A way of assigning probabilities that states that the probability of an event is equal to the number of times it has occurred in identical trials of a chance experiment, divided by the number of trials of the chance experiment.
Not a true probability model at all, this method assigns probabilities based on how likely an individual feels the event is.