Define indeterminism and compare it to determinism using what you have learned about determinism. explain how the core idea of indeterminism is closely related to the idea of causality. what example of an event that is not strictly caused and depends on chance is used? explain the example in your own words. define libertarianism, and then write an essay comparing and contrasting it to determinism, compatibilism, and indeterminism. your essay should be at least five paragraphs long.

Determinism is the idea that, given all preceding events, a later event is essentially the only possible event. In other words, given Event A, B, and C, Event D is inevitable (has a 100% probability of happening).
Indeterminism is the idea that probability, or chance, plays a role in the outcome of events, and thus no event is 100% certain to happen and thus no event is 100% predictable.
There are great implications regarding these philosophies, especially in regard to free will (do we truly control our futures?).

The core idea of indeterminism relates closely to idea of causality because it rejects the notion of perfect causality. Here's a brief and simple example:

Let's say X is the set of all life decisions you've made in your life up till now, such as how often you studied, how honest you were, whether you played sports, etc, and Y is the set of all your current "stats", such as how much money you have, whether you have a girlfriend, your grades, ETC. There is naturally a relationship between X and Y, but is it perfectly causal? If you've done everything "right" in terms of X, will Y necessarily be exactly what you want it to be? Indeterminism would propose the following (oversimplified) function:
Y = aX + ε, 
where a is some constant that relates all your daily decisions throughout life to your current situation, and ε is just a random number. There is no way to predict or control ε, so although there is a causal relationship between your actions and their outcomes, there is not perfect causality (some element of the outcome is random). 

Let's take an example form our general function above, and say that y is the probability that you got into Stanford, that Stanford only cares about grades, and x is how many hours per night you studied.
y = ax + ε
your chances increase with every hour you study, but there is also a random element of chance (ε). Your application could be lost in the mail, Stanford could get hit by an asteroid, you could have a fever during a test and get a bad grade, your principal may know the Dean of Admissions and recommend your admission (or that you aren't admitted). There is an element of chance involved with this event that is out of your control.  

The essay question is beyond the scope of and I'll leave it to you!