[scientizscht (OP)]

Hello

Is there a good quick tutorial on probabilities?

If you combine two independent events with an AND condition you multiple their probabilities.
If you combine two independent events with an OR condition you add their probabilities.

However, if you roll a dice, there is a 1/6 chance to get number 6. If you do get a 6, next time when you roll a dice will it again be 1/6 probability? What about 1,000 times?

Are there also any other concepts that are very common/funtamental and should know?

Thanks!

[Bored chemist]

next time when you roll a dice will it again be 1/6 probability?

Yes.
The dice have no memory.
How could it be anything else?
(Assuming the die is "fair")

[Eternal Student]

Hi.

Is there a good quick tutorial on probabilities?

   
   The questions you are asking look like something covered in most school courses for Mathematics up-to about age 16.
   I can't actually find an online guide that is ideal but instead would recommend you get to a library and just pick a textbook for mathematics for GCSE level mathematics and read their section on probability.    There are some websites you could use, like  BBC Bitesize  and/or   Khan Academy  if you can't get to a library.

If you combine two independent events with an AND condition you multiple their probabilities.

    That looks OK and it will be adequately explained in most texts.

If you combine two independent events with an OR condition you add their probabilities.

     This is NOT correct.    It's also slightly more advanced and might be considered part of the British Higher level GCSE Mathematics syllabus   (i.e. it's likely to be a question for the higher grades instead of just a pass grade).
      If two events were  EXCLUSIVE,   which means they never happen at the same time,  then you could add the probabilities as you have described.

Example:    You do two things:   Roll a 6-sided dice and then also flip a coin.
    Event A = "you get a 1,2 or 3 on the dice";         Event B = "You get heads from the coin toss".
   Event A and B are independent.    Whatever you get from the dice roll shouldn't influence the coin toss at all,  or vice versa.   These are two completely separate processes.
    However Event A and B are not exclusive,   you could get both events happening together.
We'll write   P(A) as usual for the probability of event A,  then    P(A) = 0.5  ;     P(B) = 0.5
However  P(A OR B)   is NOT equal to   P(A) + P(B) = 1.     It is NOT certain that you would roll a 1,2,3  or  get a head on the coin toss.   You could get a 4 on dice roll and a tail on the coin toss, for example.
    The addition of the two probabilities  P(A) + P(B)  failed to produce  P(A OR B) because the two events were NOT exclusive (it was possible for both events to happen).   This is usually explained with the use of Venn Diagrams.

However, if you roll a dice, there is a 1/6 chance to get number 6. If you do get a 6, next time when you roll a dice will it again be 1/6 probability? What about 1,000 times?

    This has already been answered by @Bored chemist  .       Yes, for a fair dice, whatever you have rolled before makes no difference to the probability of getting a result on a new roll.

Are there also any other concepts that are very common/funtamental and should know?

    Yes.       Venn Diagrams;    Exclusive Events;   Independent Events;    Tree Diagrams          These seem like key words and concepts that you should be familiar with and would usually be discussed in an elementary course on probability.   The most common examples of probability problems at this sort of level involve dice rolls and coin tosses, so it would be sensibile to practice a few examples and be familiar with common vocabulary - for example one dice is usually called a "die".  All dice are assumed to be 6 sided unless told otherwise etc.

Best Wishes.

[evan_au]

Khan Academy have courses for all levels of skill. You could start here, and pick an introductory course:
https://www.khanacademy.org/math/probability

[scientizscht (OP)]

Thanks, what about the probability of sequential events?

I assume rolling dices three times one after the other, would be very rare to return 111 and more probable to return something more random like 351

How would such concepts call? Will they be in most tutorialls?

[Bored chemist]

I assume rolling dices three times one after the other, would be very rare to return 111 and more probable to return something more random like 351

The chance of getting 351 is exactly the same as the chance of getting 111.
Any decent stats course should explain that to you.

[leoholmes]

I saw on Khan Academy and YouTube

[Spam4 0081222]

Hello

Is there a good quick tutorial on probabilities?

If you combine two independent events with an AND condition you multiple their probabilities.
If you combine two independent events with an OR condition you add their probabilities.

However, if you roll a dice, there is a 1/6 chance to get number 6. If you do get a 6, next time when you roll a dice will it again be 1/6 probability? What about 1,000 times?

Are there also any other concepts that are very common/funtamental and should know?

Thanks!

yes so helpful tutorial dear.