Probablity GRE CAT

8/4/2019 Probablity GRE CAT

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General GRE

Online Class By: Satyadhar Joshi

Probability for GRE (Level 4-5) /Quantum CAT (Level 2) / GMAT

http://www.freegregmatclass.com/
http://www.freegregmatclass.com/http://www.freegregmatclass.com/


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Content Introduction to Probability

Syllabus

Type of questions

Practice questions Conclusion

References


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Areas of Math often tested

Statistics (mean, mode, SD, range, ND, graphicalrepresentation of ND)Quadratic equations (roots, type of roots, numberof roots, positive and negative roots, etc.)

Series (AP, GP, series definition, nth term of aseries, etc.)Number theories (divisors, remainders, GCD,LCM, prime factors, number line, etc.)Probability (counting principle, basic probability,

coin and die tossing, arrangements, etc.)Speed and work problems (relation betweenspeed, distance and time, rule of 3, rule of 5, etc.)Some other concepts (ratios, inequalities, etc.)


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Introduction We would be solving questions on probability

from various sources

The toughest possible question will be solved

Target questions are 20-30 for the class withexplanation and discussion

Most comprehensive coverage and CAT levelquestions

All of three Exams easily covered To get the list of question check my uploads or

contact me at [email protected]


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Example: Flipping a coin

Whats the probability of getting heads when flipping a coin? Ans: There is onlyone way to get heads in a coin toss. Hence, the top of the probabilityfraction is 1. There are two possible results: heads or tails. Forming the

probability fraction gives 1/2.

Example: Tossing a die

Whats the probability of getting a 3 when tossing a die? Ans: A die (a cube)has six faces, numbered 1 through 6. There is only one way to get a 3.Hence, the top of the fraction is 1. There are 6 possible results: 1, 2, 3, 4, 5,

and 6. Forming the probability fraction gives 1/6.

Example: Drawing a card from a deck

Whats the probability of getting a king when drawing a card from a deck of

cards? Ans: A deck of cards has four kings, so there are 4 ways to get aking. Hence, the top of the fraction is 4. There are 52 total cards in a deck.

Forming the probability fraction gives 4/52, which reduces to 1/13. Hence,there is 1 chance in 13 of getting a king.

Example: Drawing marbles from a bowl

Whats the probability of drawing a blue marble from a bowl containing 4 red

marbles, 5 blue marbles, and 5 green marbles? Ans: There are five ways of

drawing a blue marble. Hence, the top of the fraction is 5. There are 14 (= 4+ 5 + 5 ossible results. Formin the robabilit fraction ives 5/14.


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Important Information you need toknow

Chess board is 8*8, selection of any block willuse C

Leap year has 366 days, and has 52 full weeksand 2 extra days

Considering things in one

Conditional probability in drawing


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Low scoring vs. High scoring exam

Reduction of a problem in the closest option(CAT)

Taking a go when you have more than 50% (notrecommended for GMAT and GRE because thequestions are easy)


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Permutation Permutation: In mathematics, the notion of

permutation is used with several slightly differentmeanings, all related to the act of permuting(rearranging in an ordered fashion) objects or

values. Informally, a permutation of a set ofobjects is an arrangement of those objects into aparticular order. There are six permutations of theset {1,2,3}, namely [1,2,3], [1,3,2], [2,1,3], [2,3,1],

[3,1,2], and [3,2,1].

http://en.wikipedia.org/wiki/Permutation


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Combination In mathematics a combination is a way of

selecting several things out of a larger group,where (unlike permutations) order does notmatter. In smaller cases it is possible to count the

number of combinations. For example given threefruit, an apple, orange and pear say, there arethree combinations of two that can be drawn fromthis set: an apple and a pear; an apple and an

orange; or a pear and an orange.

http://en.wikipedia.org/wiki/Combination


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Axiomatic Approach to ProbabilityTheorem

DefinitionThe sample space, denoted by , is the collection or

totality of all possible outcomes of a conceptualexperiment.

Toss of a coin twice := {HH, HT, TH, TT}

Definition

An event, is a subset of the sample space. Theclass of all events associated with a givenexperiment is defined to be the event space. Weusually denote the event space by F.

http://www.tutornext.com/axiomatic-approach-some-theorems-

http://en.wikibooks.org/wiki/Probability/Introduction#Axiomatic_probability_theor

y

http://myweb.polyu.edu.hk/~majlee/AMA372/lec1_4.pdf


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Conditional Probability Conditional probability is the probability of

some eventA, given the occurrence of someother event B. Conditional probability is writtenP(A|B), and is read "the (conditional) probability

of A, given B" or "the probability of A under thecondition B". When in a random experiment theevent B is known to have occurred, the possibleoutcomes of the experiment are reduced to B,

and hence the probability of the occurrence of Ais changed from the unconditional probability intothe conditional probability given B.

http://en.wikipedia.org/wiki/Bayesian_probabilityhttp://en.wikipedia.org/wiki/Bayes%27_theorem

http://en.wikipedia.org/wiki/Conditional_probabil

ity

http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter4.pdf
http://en.wikipedia.org/wiki/Probabilityhttp://en.wikipedia.org/wiki/Event_(probability_theory)http://en.wikipedia.org/wiki/Event_(probability_theory)http://en.wikipedia.org/wiki/Probability


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Multiplication Theorem

The multiplicationtheorem is used to answer the following questions:

What is the probability of two or more events occurring either

simultaneouslyor in succession?

For two events A and B: What is the probability of event A and eventB

occurring?

The individual probability values are simply multiplied to arrive at theanswer. The word

and is the key word that indicates multiplication of the individualprobabilities. The

multiplicationtheorem is applicable only if the events areindependent. It is not valid

when dealing with conditional events. The product of two or moreprobability values

yields the intersection or common area of the probabilities. Mutuallyexclusive events do not

have an intersection or common area. The probability of two or moremutually exclusive

events is always zero.http://cqeweb.com/previews/chapter3_preview.pdf


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Binomial Theorem in Probability

A binomial experiment is one that possesses thefollowing properties:

1.The experiment consists of nrepeated trials;

2.Each trial results in an outcome that may be classifiedas a success or a failure (hence the name, binomial);

3.The probability of a success, denoted by p, remainsconstant from trial to trial and repeated trials areindependent.

The number of successes X in ntrials of a binomialexperiment is called a binomial random variable.

The probability distribution of the random variable X iscalled a binomial distribution, and is given by theformula:

P(X) = Cnxpxqnx where

Cnx

is a combination

http://www.amscopub.com/%5Cimages%5Cfile%5CFile_671


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In mathematics a combination is a way of selecting

several things out of a larger group, where (unlike

permutations) order does not matter. In smaller cases it

is possible to count the number of combinations. For

example given three fruit, an apple, orange and pear say,

there are three combinations of two that can be drawn

from this set: an apple and a pear; an apple and an

orange; or a pear and an orange. More formally a k-

combinationof a set S is a subset ofkdistinct elements

of S. If the set has n elements the number of k-

combinations is equal to the binomial coefficient

which can be written using factorials aswhenever , and which is zero when k> n.


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Bayes Theorem

Thomas Bayes addressed both the case of discrete probability distributions of

data and the more complicated case of continuous probability distributions. In the

discrete case, Bayes' theorem relates the conditional and marginal probabilities of

eventsA and B, provided that the probability ofB does not equal zero:

In Bayes' theorem, each probability has a conventional name:

P(A) is thepriorprobability (or "unconditional" or "marginal" probability)ofA. It is "prior" in the sense that it does not take into account any

information about B; however, the event B need not occur after eventA. In

the nineteenth century, the unconditional probability P(A) in Bayes's rule

was called the "antecedent" probability;[3]

in deductive logic, the

antecedent set of propositions and the inference ruleimplyconsequences.

The unconditional probability P(A) was called "a priori" by Ronald A. Fisher.

P(A|B) is the conditional probability ofA, given B. It is also called theposterior probability because it is derived from or depends upon the

specified value ofB.

P(B|A) is the conditional probability ofB givenA. It is also called thelikelihood.

P(B) is the prior or marginal probability ofB, and acts as a normalizingconstant.

'


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Conditional Probability

Conditional probabilityis the probability of some eventA, given

the occurrence of some other event B. Conditional probability

is written P(A|B), and is read "the probability ofA, given B". It is

defined by

IfP(B) = 0 then is undefined.


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Addition Rule for Probability

If either event A or event B or both events occur on a single performance of an

experiment this is called the union of the events A and B denoted as . If

two events are mutually exclusive then the probability of either occurring is

For example, the chance of rolling a 1 or 2 on a six-sided die is

If the events are not mutually exclusive then

For example, when drawing a single card at random from a regular deck of cards,

the chance of getting a heart or a face card (J,Q,K) (or one that is both) is

, because of the 52 cards of a deck 13 are hearts, 12 are face

cards, and 3 are both: here the possibilities included in the "3 that are both" are

included in each of the "13 hearts" and the "12 face cards" but should only be

counted once.


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Questions A

Quantum CAT Level 2type question (similarquestions with different

data and language)


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Questions B GRE Nova MathBible (similar

questions withdifferent dataand language)

(Buy the bookwhich isrequisite for thisclass athttp://novapress.net/)

Without gettingthis book youare notsupposed toland in my class


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Conclusion All problems of all level illustrated

Helpful in all major exams

Email me at [email protected] for any doubts

Do register for future classes http://onlineclasses.nanotechbiz.org/
mailto:[email protected]:[email protected]


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References GRE Math Bible Nova GMAT Nova Bible

Arihant Quantum CAT For Admission into IIMs

Quantitative CAT Arun Sharma, TMH

Documents

Probablity GRE CAT