What are the formulas for solving sets A and B?

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SUMMARY

The discussion focuses on the mathematical formulas for solving problems related to sets A and B, specifically in the context of probability. Key formulas mentioned include the General Addition Rule, Special Addition Rule, and Conditional Probability. The participants clarify the symbolic representations of set operations, such as $A^c \cap B^c$ for "not A and not B," and discuss the need for clear mathematical notation for exam preparation. The conversation emphasizes the importance of understanding these formulas for successfully answering exam questions.

PREREQUISITES
  • Understanding of set theory notation, including symbols like $\cup$ and $\cap$
  • Familiarity with basic probability concepts and rules
  • Knowledge of conditional probability and independence in events
  • Ability to interpret mathematical expressions related to sets
NEXT STEPS
  • Study the General Addition Rule in probability: P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
  • Learn about Conditional Probability: P(A | B) = P(A ∩ B) / P(B)
  • Review the Special Addition Rule for mutually exclusive events: P(A ∩ B) = ∅
  • Practice solving problems involving set operations and their probabilities using symbolic notation
USEFUL FOR

Students preparing for exams in probability and set theory, particularly those needing to memorize formulas for solving problems involving sets A and B.

nickar1172
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Which formula's would you use to solve each set and please show the actual formulas please thank you for the help I really appreciate it as I need to know this for my final exam tomorrow, thank you!

a) solving for neither set A and neither set B b) Solving for set A or Set B, but not bothc) Solving for set B given set Ad) Solving for set B given that he does not have Set A
 
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Hi again,

I probably need some more information. Are you simply asked to write these concepts mathematically, like $A \cap B$?
 
Jameson said:
Hi again,

I probably need some more information. Are you simply asked to write these concepts mathematically, like $A \cap B$?

Yes that is exactly what I am talking about
 
nickar1172 said:
Yes that is exactly what I am talking about

Ok well we can use $A, A^c, B, B^c$ for referring to the sets and we can also use $\cup, \cap$. What do you get for the first one?

(by the way, $\cup$ means "or" and $\cap$ means "and")
 
If I new I wouldn't be asking the question...
Postulates for Probability - P(A) >= 0, P(S) = 1
Special Addition Rule (mutually exclusive) - If A ∩ B = ∅, then P(A ∪ B) = P(A) + P(B)
General Addition Rule - P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
Probability and Odds (odds of A to B) - a / (a + b)
Conditional Probability - P(A | B) = P(A ∩ B) / P(B) provided that P(B) ≠ 0
General Multiplication Rule - P(A ∩ B) = P(A) . P(B | A)
Special Multiplication Rule(Independent events) - P(A ∩ B) = P(A) . P(B)
Multiplication Rules - if event B is independent of event A, then P(B | A) = P(A)

according to any of these rules how do you answer those question because I have NO IDEA how to
 
I didn't ask you what the correct answer was, rather what you think it is. If I just give you the answer that isn't helping you very much. We try to help you learn the material so you can answer it yourself. :)

Ok, (a) is $A^c \cap B^c$. Put into words this is "not A and not B". For (b), what is "A or B" in symbolic language? What is "A and B"?
 
I know what and or means I just need to know how to solve those questions, at this point it is not about "understanding" anything I just need to put this down on a formula sheet these answers so when I see this on the exam I know what to plug in like a machine, the entire semester has passed and I still don't know and I don't want to understand I just want to get an 80 on my test tomorrow so I don't fail the class all I need is those answered in mathematical notation if you can help me than I greatly appreciate it if not than no problem
 

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