5.2 Introduction to probability

  1. What does P(A)=0 and same but =1 mean?
    Either it will for sure happen or it will for sure not happen
  2. What is a sample space and how is it denoted?
    it is denoted by S and it the set of all possible outcomes by an experiment.
  3. How wo we calissify subgrops of S? the sample space
    If it is a subgrpup it is a specific event and that we donte as E
  4. What is a union of two events? sign?
    • It is the probability of all outcomes that are in one or in both of the unioned outcomes.
    • Denoted by U , similar to V as in OR logic, it could be either or both. U & V both has 1 point ruching the ground.
  5. What is the intersection of two events called?
    denoted as ?
    • The intersection of two sets of outcomes means the probability of an event that is in both of them.
    • Denoted as ^ but u fomed.
    • Has two pints in the ground just like an "and" meaning outcome must be in both outcome sets
  6. When are two probability sets  mutually exclusive?
    When their intersection = 0.
  7. What is the compliment of an event?
    It is all the other possible outcomes that are not in the set being complimented.
  8. Fot two sets of outcomes say A and B when is A contained in B?
    When all outcomes that are in set A are also in set B and B has outcomes that are not in set A
  9. What does in U on its side mean?
    It mean that one of the sets are contained in the other. The pointing part of the U(here bottom part) shows the set being contained.
  10. What are the three axioms of probability?
    • 1: The probability of an outcome/ set of outcomes are between 1 and 0.
    • 2. With probability 1 the outcome will be a member of the sample space 1.
    • 3. For any sequance of mutually exclusive events of outcomes, the sum of all of them will be equal to 1. (each dice has a 16.666 chance of occuring and together they all add up to 1.)
  11. What does the odds mean and how are they calculated?
    • It represents how much more likely an event is to occur in relation to it not occurring.
    • odds of event A occurring would be
    • P(A)/P(A`) where the denominator is the compliment of A.
  12. How do we calculate the probability of an event with very large sample space S?
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  13. What is conditional probability?
    How is it calculated if B is conditioned on A
    • A probability can be calculated by also including the event of another event occuring(or not occuring) .
    • P(B|A) means prob of B occurring given that A has occurred.
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  14. How do we count with replacement?
    example?
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    • For a numbers lock we have 10 digis and 3 rotating discks with them then We have 10*10*10
  15. How do we count permutation?
    With or without replacement?
    • They are without replacment
    • we have a sample size N and the solve for how many different ways we can select R number of n´s .
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  16. What is Bays theorem and what is it used for?
    Based on?
    • Calculating when (A|B) is hard and we would prefer (B|A), We can do this using Bays theorem.
    • Based on two conditional probabilities calculation, one with A|B and then B|A using this Image Upload 5
    • to get this Image Upload 6
  17. What is the difference of combinations and permutations? What generates the largest value on a given set?
    • Permuations sounds more complex bc it is and therefor generats a higher number then combinations. This is because order matters in permuations so ABC notequalto ACB
    • In both cases we have two varibles N & R but in permuations the order
  18. What is the formula for permutations and give a word problem so describe each variables role.

    Without Repetition
    Without Repetition


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    • We have 8 ppl and 3 medals(Gold,Silver,Bronze) , how many ways can we hand out the medals to these people?
  19. What is the formula for Combinations and give a word problem so describe each variables role.

    Without replacement
    Without replacement 

    Here order does not matter (ABC = ACB) = T.



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  20. What is the formula for permutations and give a word problem so describe each variables role.

    Without Repetition
    Image Upload 9
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5.2 Introduction to probability
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