what's the name and formula for this prob theory?

Hello - Can you please help me with the following?:

You have 2 independent events, each with a 75% probability of success. What is the probability of both events being successful? I think the formula for this would be .75 * .75 = 56%

Can you remember the name of this probability theory? I checked Wikipedia but it listed a dozen different probability theories and I couldn't hash through them all.

What about the same scenario but event B is dependent on the successful completion of event A? What's the specific name of that probability theory and what's the associated mathematical formula?

Re: what's the name and formula for this prob theory?

If the events are independent, say A and B, then

P(A and B) = P(A)P(B)

If B is dependent on A, then

P(A and B) = P(A given B)P(B)

If you wanted to just use the second one in all cases that's fine since if A is independent on B, then P(A given B) = P(A)

Re: what's the name and formula for this prob theory?

Thanks Mac - I understand case 1:

if p(a) = .80 and p(b) = .80 then

p(a)p(b) = .80 * .80 = .64

So I can say the probability of both a and b is 64%.

However, I'm unclear on how to breakdown case 2 into more concrete terms. Can you please provide an example?

Re: what's the name and formula for this prob theory?

A quick search yielded this site, which I found useful. It states the same equation that I stated but re-wrote it.

From the site we get some good examples, like with example #1 involving marbles.

Conditional Probability

However it should be noted that sometimes the conditional probability P(A|B) is not given. Otherwise it is simple algebra. There is also a generalization of independence/dependence of statistical variables with calculus for more complex cases.

Re: what's the name and formula for this prob theory?

Thanks Mac - I can tell you have strong domain knowledge of probability theory. Is there a special name for 1 event probability within a total probability calculation ?

probability event?

probability dependency?

probability condition?

probability data point?

I'm trying to describe in an email how each of these probability events is a dependency/constraint against the total probability and how removing 1 of these probability events will improve the total probability and I'd like to use the most appropriate terminology....

Re: what's the name and formula for this prob theory?

The name you should have looked for is just 'independent events'. As Macsters Undead said, two events, A and B, are "independent" if and only if Prob(A and B)= Prob(A)Prob(B).

Re: what's the name and formula for this prob theory?

Thanks halls - great answer. I think for the purpose of my email I'll just refer to it as an "event" instead of "independent event." My logic for this is (and please correct me if I'm wrong) that a dependent event will impact total probability even more than an independent event.

So mentioning event "independence" would be superfluous in the context of my email because removing any event (independent or dependent) would impact total probability.

My main goal is to introduce probability theory into an organization so it's important to keep my initial message as simple and straightforward as possible. Unless you see any holes in this logic....

Re: what's the name and formula for this prob theory?

Is there standard/proper terminology to refer to all the events being considered for total probability?:

event set?

event collection?