1. General GRE Online Class By: Satyadhar Joshi Probability for GRE (Level 4-5) / Quantum CAT (Level 2) / GMAT http://onlineclasses.nanotechbiz.org

2. Content Introduction to Probability Syllabus Type of questions Practice questions Conclusion References

3. Areas of Math often tested Statistics (mean, mode, SD, range, ND, graphical representation of ND) Quadratic equations (roots, type of roots, number of roots, positive and negative roots, etc.) Series (AP, GP, series definition, nth term of a series, 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 between speed, distance and time, rule of 3, rule of 5, etc.) Some other concepts (ratios, inequalities, etc.)

4. 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 with explanation and discussion Most comprehensive coverage and CAT level questions All of three Exams easily covered To get the list of question check my uploads or contact me at shivgan3@yahoo.com

5. Example: Flipping a coin What’s the probability of getting heads when flipping a coin? Ans: There is only one way to get heads in a coin toss. Hence, the top of the probability fraction is 1. There are two possible results: heads or tails. Forming the probability fraction gives 1/2. Example: Tossing a die What’s 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 What’s 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 a king. 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 What’s 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)possible results. Forming the probability fraction gives 5/14.

6. Important Information you need to know Chess board is 8*8, selection of any block will use “C” Leap year has 366 days, and has 52 full weeks and 2 extra days Considering things in one Conditional probability in drawing

7. Low scoring vs. High scoring exam Reduction of a problem in the closest option (CAT) Taking a go when you have more than 50% (not recommended for GMAT and GRE because the questions are easy)

8. Permutation Permutation: In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting (rearranging in an ordered fashion) objects or values. Informally, a permutation of a set of objects is an arrangement of those objects into a particular order. There are six permutations of the set {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

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

10. Axiomatic Approach to Probability Theorem Definition The sample space, denoted by, is the collection or totality of all possible outcomes of a conceptual experiment. Toss of a coin twice : = {HH, HT, TH, TT} Definition An event, is a subset of the sample space. The class of all events associated with a given experiment is defined to be the event space. We usually denote the event space by F. http://www.tutornext.com/axiomatic-approach-some-theorems-probability/1443 http://en.wikibooks.org/wiki/Probability/Introduction#Axiomatic_probability_theory http://myweb.polyu.edu.hk/~majlee/AMA372/lec1_4.pdf

11. Conditional Probability Conditional probability is the probability of some event A, given the occurrence of some other event B. Conditional probability is written P(A|B), and is read "the (conditional) probability of A, given B" or "the probability of A under the condition B". When in a random experiment the event B is known to have occurred, the possible outcomes of the experiment are reduced to B, and hence the probability of the occurrence of A is changed from the unconditional probability into the conditional probability given B.probabilityevent http://en.wikipedia.org/wiki/Bayesian_probability http://en.wikipedia.org/wiki/Bayes%27_theorem http://en.wikipedia.org/wiki/Conditional_probability http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter4.pdf

12. Multiplication Theorem The multiplication theorem is used to answer the following questions: What is the probability of two or more events occurring either simultaneously or in succession? For two events A and B: What is the probability of event A and event B occurring? The individual probability values are simply multiplied to arrive at the answer. The word “and” is the key word that indicates multiplication of the individual probabilities. The multiplication theorem is applicable only if the events are independent. It is not valid when dealing with conditional events. The product of two or more probability values yields the intersection or common area of the probabilities. Mutually exclusive events do not have an intersection or common area. The probability of two or more mutually exclusive events is always zero. For mutually exclusive events: P(A) and P(B) = 0 For independent events: Probability (A and B) = P(A) and P(B) = P(A) X P(B) http://cqeweb.com/previews/chapter3_preview.pdf

13. Binomial Theorem in Probability A binomial experiment is one that possesses the following properties: 1. The experiment consists of n repeated trials; 2. Each trial results in an outcome that may be classified as a success or a failure (hence the name, binomial); 3. The probability of a success, denoted by p, remains constant from trial to trial and repeated trials are independent. The number of successes X in n trials of a binomial experiment is called a binomial random variable. The probability distribution of the random variable X is called a binomial distribution, and is given by the formula: P(X) = C n x p x q n−x where C n x is a combination http://www.amscopub.com/%5Cimages%5Cfile%5CFile_671.pdf

18. Questions A Quantum CAT Level 2 type question (similar questions with different data and language)

19. Questions B GRE Nova Math Bible (similar questions with different data and language) (Buy the book which is requisite for this class at http://novapress.ne t/) Without getting this book you are not supposed to land in my class

20. Conclusion All problems of all level illustrated Helpful in all major exams Email me at shivgan3@yahoo.com for any doubtsshivgan3@yahoo.com Do register for future classes http://onlineclasses.nanotechbiz.org/

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22. References GRE Math Bible Nova GMAT Nova Bible Arihant Quantum CAT For Admission into IIMs Quantitative CAT Arun Sharma, TMH