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(MATH) > PROBABILITY > Flashcards

PROBABILITY Flashcards

1
Q

branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

A

PROBABILITY

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2
Q

base formula for PROBABILITY

A

P= NUMBER OF DESIRABLE OUTCOMES / NUMBER OF ALL POSSIBLE OUTCOMES.

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3
Q

1st princicple of counting;
IN PROBABILITY WHEN AN EVENT CAN BE DONE IN M DIFFERENT WAYS AND ANOTHER EVENT CAN BE DONE IN N DIFFERENT WAYS, THEN THESE TWO EVENTS ‘CAN’ BE DONE ONE AFTER THE OTHER.

how does this two event relate through mathematical expression

A

M X N

  • THE WORD “AND” IS USUALLY THE INDICATOR FOR MULTIPLICATION
  • becuase all events will happen
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4
Q

2nd princicple of counting;
IN PROBABILITY WHEN AN EVENT CAN BE DONE IN M DIFFERENT WAYS AND ANOTHER EVENT CAN BE DONE IN N DIFFERENT WAYS, THEN THESE TWO EVENTS ‘CAN’ BE DONE IN TWO SEPARATE WAYS

how does this two event relate through mathematical expression

A

M + N

  • THE WORD “or” IS USUALLY THE INDICATOR FOR addition
  • only 1 event will occur
  • SUBTRACTION IS ALSO USED IF THERE ARE REPEATING EVENT!!!
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5
Q

an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements.

A

permutation

-order is important! meaning arrangement 1-2 is different as 2-1
“combination lock should be called permutation lock because 123 is NOT the same as 213 in a real life combination lock”

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6
Q

formulae for PERMUTATION and explain each

A 
nPr = n!/(n-r)! =when n objects is arranged at r at a time
nPn= n! =when n objest is arranged at n time as well
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7
Q

THE NUMBER OF POSSIBLE OUTCOME = ____+ ____?

A

UNDSIRABLE OUTCOME + DESIRABLE OUTCOME!

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8
Q

the shifting of an entire of elements one or more stapes forward or backwards without without changing the order of the elements in the sequence.

A

CYCLIC PERMUTATION

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9
Q

formulas for cyclic permutation and explain each

A

nPr/r =when n objects is arranged at r at a time

nPn/n= (n-1)! =when n objest is arranged at n time as well

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10
Q

the number of permutation _____ when a collection contains identical elements

A

are REDUCED!

LIKE word arrangements, because M I S S is still M I SS when you switch the letter S, right?!?

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11
Q

GIVE THE FORMULA WHERE THE PERMUTATION OS N OBJECTS TAKEN ALL AT ONCE WITH P,Q,&S THINGS ALIKE…

LIKE WORD ARRANGEMENT WITH REPEATING LETTERs

A

n!/p!q!s!

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12
Q

is a selection of all or part of a set of objects, without regard to the order in which objects are selected.

A

combination

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13
Q

formula of Conbination

A

n!/r!(n-r)!

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14
Q

two or more events that can never happen in the same trial.

A

MUTUALLY EXCLUSIVE

THIS IS ONLY APPLICABLE FOR ADDITION RULE! (OR)
WHICH STATES
Pr + Pb = (P r or b)= P(rub)

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15
Q

two or more events that can happen in the same trial.

A

non mutually exclusive

also applies to ADDITION RULE! (OR)
with the formula
P(AorB)= P(AUB)= P(A)+P(B)-P(AnB)

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16
Q

IF THE OUTCOME OF ONE TRIAL DOES NOT AFFECT THE OUTCOME OF OTHER TRIALS THEN IT IS CALLED _____

A

INDEPENDENT EVENTS

muliplication rule is applied
P(AnB) = P(A) X P(B)

17
Q

IF THE OUTCOME OF ONE TRIAL “AFFECTS” THE OUTCOME OF OTHER TRIALS THEN IT IS CALLED _____

A

DEPENDENT EVENTS

also applies mltiplication rule
given the formula;
P(B|A)= P(B GIVEN A)

P(AnB)= P(A) X P(B|A)

18
Q

A MEASURE OF THE PROBABILITY OF AN EVENT OCCURING GIVEN THAT ANOTHER EVENT HAS OCCURED

A

CONDITIONAL PROBABILITY

-INTRODUCED BY THOMAS BAYES
P(A|B) = P(AnB)/P(B)

19
Q

A CONDITIONAL RULE SAYS THAT, THE PROBABILITY OF A GIVEN B MULTIPLIED BY THE PROBABILITY OF OF B IS EQUAL TO ?

A

PROBABILITY OF B GIVEN A MULTIPLIED BY THE PROBABILITY OF A.

20
Q

A “FREQUENCY DISTRIBUTION” OF THE POSSIBLE “NUMBER OF SUCCESSFUL OUTCOMES” IN A GIVEN NUMBER OF TRIALS IN EACH OF WHICH THERE IS THE “SAME PROBABILITY OF SUCCESS”

A

BINOMIAL DISTRIBUTION

-APPLICABLE FOR REPEATED TRIALS

21
Q

4 CHARACTERISTICS OF A BINOMIAL DISTRIBUTION.

A
  • an event is repeated in a fix number of trials
  • only two possible outcomes “bi”
  • the probability of success is same in each trial
  • each trial is independent of each trial
22
Q

BINOMIAL DISTRIBUTION FORMULA

A

P = (nCr )(p^r) q^(n-r)

P	=	binomial probability
r	=	number of successful trials
p	=	probability of success on a single trial
q	=	probability of failure on a single trial
n	=	number of trials

*where p + q = 1

23
Q

a DISCRETE PROBABILITY DISTRIBUTION OF THE NUMBER OF EVENTS OCCURING IN A GIVEN TIME PERIOD, GIVEN THE AVERAGE NUMBER OF TIMES THE EVENT OCCURS OVER THAT TIME PERIOD

A

POISSON DISTRIBUTION.

– SIMILAR TO BINOMIAL DIST, BUT WITH A GIVEN TIME PERIOD.

24
Q

4 CHARACTERISTICS OF POISSON DISTRIBUTION

A
  • an event can occur any number of times in during
    a time period
  • event occur independently
  • the rate of occurence is constant
  • the probability of an event occuring is proportional to the length of the time period
25
Q

POISSON FORMULA IS ????? STATE THE FORMULA!!!

A

P(x=k) = (λ^k) (e^-λ) / k!

k= number of (events observed/successful trial) in a given time period.
λ= expected value or (average/mean) of X

λ=np = MEAN
where, n= total number of trial & p= probability of success

σ = npq = VARIANCE
where q= probability of failure.

26
Q

IN ORDER TO APPLY POISSON DISTRIBUTION FORMULA, THE VAULE OF λ MUST BE?

A

λ<10

27
Q

A PROBABILITY FUNCTION THAT DESCRIBES HOW THE VALUES ARE DISTRIBUTED. A SYMMETRIC DISTRIBUTION WHERE MOST OF THE OBSERVATIONS CLUSTERS AT THE CENTRAL PEAK

A

NORMAL DISTRIBUTION

MEAN=MODE=MEDIAN

28
Q

DIFFERENTIATE MEAN MEDIAN AND MODE

A

MEAN= AVERAGE
MEDIAN= THE MIDDLE VALUE FROM THE SET.
MODE= NUMBER THAT REPEATS THE MOST
RANGE=HIGHEST - LOWEST VALUE IN A SET.

29
Q

4 PROPERTIES OF NORMAL DISTRIBUTION

A
  • SYMMETRIC AT THE CENTER
  • MEAN MEDIAN MODE IS EQUAL
  • EX ATCLY HALF OF THE VALUE IS IN THE LEFT & RIGHT OF THE CENTER

THE TOTAL AREA UNDER THE CURVE IS 1-

30
Q

FOR NORMAL DISTRIBUTION, THIS GIVES THE IDEA OF HOW FAR FROM THE MEAN A DATA POINT IS.

A

Z- SCORE, STANDARD SCORE

31
Q

FORMULA FOR Z-SCORE

A

z=x-µ/σ
µ= MEAN
x=GIVEN VALUE
σ=standard dev

32
Q

for normal distribution, formula for area to the left of (z =a) .probability where (a>z)

A

P(a>z)= ∫(-∞,a) [1/√(2π) e^(-z^2/2) dz

P(az)

33
Q

GIVEN VALUES TO USE;
BINOMIAL DISTRIBUTION-
POISSON’S DISTRIBUTION-
NORMAL DISTIBUTION-`

A

BINOMIAL DISTRIBUTION- PROBABILITY OF ONE SUCCESSFUL TRIAL

POISSON’S DISTRIBUTION- EXPECTED VALUE

NORMAL DISTIBUTION-`MEAN & STANDARD DEV.

34
Q

_____ IS A FORMULA FOR DETERMINING CONDITIONAL PROBABILITY THAT ALLOWS US TO UPDATE PREDICTED PROBABILITY OF AN EVENT BY ADDING IN NEW EVIDENCES.

A

BAYES THEOREM

35
Q

BAYES THEOREM FORMULA

A

P(H|E)=[P(E|H)P(H)] / P(E)`

P(h) = previous likelihood
P(e|H) = probability you want to know
P(E) = total probability
36
Q

probabillity of having at least 1/2/3 ….

a helpful equation can be ___

A

1 - ( opposite probability, e.g none where picked)

(MATH) (11 decks)

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