Probability

Formulas/Rules:

P(A U B): Probability of A OR B

  • whenever the formula has OR, you add A & B together

  • formula doesn’t work for mutually exclusive events (you have to use the formula below this)

P(A) + P(B) - P(A ∩ B): Probability of A OR B MINUS probability of A AND B

  • this is the formula you use when you have an overlap for an OR problem and you’re trying to find the probability of A or B (probability of A or B MINUS the overlap aka the ones that are BOTH A and B)

  • formula DOES work for mutually exclusive events

  • general addition rule

P(A ∩ B): Probability of A AND B

  • whenever the formula has AND, you look for ONE number that is in both categories, both qualities have to be true

  • Ex. P(Even ∩ Red) —> we’re looking for all chips that are BOTH even and red

P(A) x P(B | A) = P(A ∩ B): Probability of A TIMES probability of B EQUALS probability of A AND B

  • this is the formula you use to find the overlap/middle section of ven diagram

  • formula DOES work for mutually exclusive events

  • general multiplication rule

P(A | B): Probability of A GIVEN B

  • whenever the formula has GIVEN, the GIVEN info (B) is the denominator and the info we’re finding (A) is the numerator 

  • Ex. P(Red | Even) —> 5/10 chips are even so 5 is the denominator, 2/5 red chips are even. So, we the final answer is 2/5 (2 chips out of all 5 even chips are red)

  • Denominator is not the entire amount, only the given amount!! (so the denominator changes in given problem)

P(A) = P(A | B): Probability of A EQUALS probability of A GIVEN B

P(A) x P(B) = P(A ∩ B): Probability of A TIMES probability of B EQUALS probability of A AND B

  • these formulas are used to CHECK FOR INDEPENDENCE

Concepts:

  • mutually exclusive/disjoint = things can’t happen at the same time (ex. a poker chip cannot be green and red at the same time) —> When events are mutually exclusive, they CANNOT BE INDEPENDENT

  • independent = events do NOT affect the probability of each other (if the two probability’s equal each other when you check, it means they ARE independent)

  • associated = whenever events are NOT independent, they are associated (they effect each other)