Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Indeterminism wikipedia , lookup
History of randomness wikipedia , lookup
Random variable wikipedia , lookup
Dempster–Shafer theory wikipedia , lookup
Probability box wikipedia , lookup
Infinite monkey theorem wikipedia , lookup
Conditioning (probability) wikipedia , lookup
Law of large numbers wikipedia , lookup
Inductive probability wikipedia , lookup
Birthday problem wikipedia , lookup
Probability P(A)=n(A)/n(S) n(AB)=n(A)+n(B)-n(AB) P(AB)=P(A)+P(B)-P(AB) Some terminology and their diagrams At most one of A and B Exactly one of A and B At least one of A and B Both A and B Conditional Probability P(A/B)=P(AB)/P(B) Where P(A/B) is defined as the probability of occurrence of event A given that event B has already occurred Independent Events If event A is independent of B P(A/B)=P(A) P(AB)=P(A)P(B) and similarly P(A1A2A3………..)=P(A1)P(A2)P(A3)………… The result P(A1A2 A3………..)=1P(A`1)P(A`2)P(A`3)………… follows from the previous one. Mutually Exclusive Events P(AB)=0 P(AB`)=P(A)- P(AB) By Venn diagran Geometrical methods of probability P{xA}=Measure of region A/Measure of samplespace Baye’s Theorem n(A)=n(AiA) where I varies from 1 to r P(A)=P(AiA) where I varies from 1 to r = P(Ai/A)P(A) Inverse probability P(Ai/A)= P(AiA) /P(A)=P(A/Ai).P(Ai)/ P(Ai/A)P(A) Binomial Probability N successive independent events having only two results P and Q with probability p and 1-p then the probability of r P’s will be P(E)= nCrpr(1-p) n-r Q. A and B are two events .The probability that at most one of A,B occurs is (a)1- P(AB) (b)P(A’)+P(B’)- P(A’B’) (c)P(A’)+P(B’)+ P(AB)-1 (d) P(AB’)+ P(A’B)+ P(A’B’) Q.Three numbers are selected at random without replacement from the set of the numbers {1,2,….n}.The conditional probability that the third number lies between the first two number is known to be smaller than the second is (a)1/6 (b)1/3 (c)1/2 (d)none of these Q.Seven digits from the numbers 1,2,3,4,5,6,7,8,9 are written in random order,the probability that this seven digit number is divisible by 9 is ___________. JEE 2005 Screening Question: Q.A six faced fair dice is thrown until 1 comes, then the probability that 1 comes in even no. of trials is (a)5/11 (b)5/6 (c)6/11 (d)1/6 Mains Question Q.A person goes to office either by car,scooter,bus or train probability of which being 1/7,3/7,2/7,and 1/7 respectively.Probability that he reaches office late,if he takes car,scooter,bus or train is 2/9,1/9,4/9 and 1/9 respectively.Given that he reached office in time,then what is the probability that he travelled by a car.