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45 Cards in this Set
- Front
- Back
- 3rd side (hint)
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A - B =
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A intersect (∩) B' (compliment)
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U - A =
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U intersect (∩) A' (compliment)
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U - B'
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U intersect (∩) B
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elements of A & B formula ...
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n(A union(∪) B) = n(A) + n(B) - n(A intersect (∩) B)
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Subsets to elements
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2 ^x =subsets
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subsets have all the dolls including the big one. Symbol C with underline.
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Proper Subsets to elements:
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2 ^x -1 =proper subsets
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Proper subsets are bald just C by it self, are the dolls for the inside.
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Tip: when problem with Venn Diagrams
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List out A, B, C and A', B', and C'
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Conjunction
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p (∧) q = and, but, nor
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Disjunction
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p (∨) q = or, otherwise
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negate p
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(squiggly) p
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negate = opposite of whatever P is
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Negate: ~ (p (∧) q) =
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not p or not q = ~pV~q
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change signs, flip symbols
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Negate: ~ (p (∨) q) =
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not p and not q = ~p∧~q
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change signs, flip symbols
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Truth Tables: p (∧) q
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rule. P = true. Q = true. = true. otherwise answer is false.
T T T T F F F T F F F F |
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Truth Tables: p (∨) q
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rule. P = false. Q= false. =FALSE.
otherwise answer is true. T T T T F T F T T F F F |
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Truth Tables: V
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rule. if one is true, then its true.
T T T T F T F T T F F F |
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P <~~> Q
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Equivalent
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Conditional
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P ~~> Q
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Truth Tables: p ~> q
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If P (true), Then Q(false) = False. Otherwise True
T T T T F F F T T F F T |
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Converse
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q ~> p
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C C I C
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Inverse
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~p->~q
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CCIC
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Contrapositive
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~q~>~p
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CCIC
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Bi Conditional
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P <~>Q
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Truth Tables: P <~> Q
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rule. If P (true), then Q (true) It is true. If P (false), then Q (false) It is true. Otherwise false.
T T T T F F F T F F F T |
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In how many ways =
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Whole Numbers
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Permutation
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order matters
WITHOUT REPLACEMENT Calc: nPr By Hand: 26 x 25 x 24 |
two important things to know
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Combination
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order doesn't matter
Calc: nCr |
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Mutually Exclusive ..?
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means to not occur at the same time
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if two things cant happen at the same time the intersection is 0
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finding two combinations means to.. C(X,Y) ___ C(X,Y) =
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multiply
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no repetition allowed means
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throw back in the pile
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OR =
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ADD
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AND =
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MULTIPLY
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Probability means..
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draw fraction line
find sample space ask if order matters? draw tree diagram |
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DICE means..
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order always matters
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Independent Events
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list out both sides (ex. pass fail. defective/not defective)
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at least one MALE =
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1 - P(NONE MALES)
which also means 1 - P(ALL FEMALES) |
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probability that sum is [any number ex. 5]
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list all numbers
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To find z-score
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Z= X - Xi (mean) / @ (SD)
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Favorable Probability - when in fraction mode
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F / F + U
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Favorable Odds
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F to U
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Odds Against
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U to F
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hint: to solve odds against
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do odds in favor first
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Odds to Probability
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f to u
fill in f/f+u solve. |
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test scores & z-scores:
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further from the mean the better
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Use the Table means
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Use the Table.
Find Zscore correspondent to probability chance (0.249) |
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Use the Table Question: less than [any number for ex. 60]
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find z score
corresspond to .. [0.249] subtract from 0.5 = answer. |
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