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What does P(A)=0 and same but =1 mean?
Either it will for sure happen or it will for sure not happen
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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.
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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
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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.
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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
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When are two probability sets mutually exclusive?
When their intersection = 0.
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What is the compliment of an event?
It is all the other possible outcomes that are not in the set being complimented.
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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
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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.
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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.)
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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.
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How do we calculate the probability of an event with very large sample space S?
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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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How do we count with replacement?
example?
- For a numbers lock we have 10 digis and 3 rotating discks with them then We have 10*10*10
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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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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
- to get this
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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
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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?
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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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What is the formula for permutations and give a word problem so describe each variables role.
Without Repetition
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