Conditional Probability of event A conditioned on the fact that event B has happened is called the conditional probability and written as P(AIB).# T H6 N8 q r& _' V) G
P(AIB)=Probability Both A and B happens/ Probability B happens." F% Q3 p% b) j
Example: v. G: o- y$ q5 k( ?9 p' | A six-sided die with faces from 1 to 6 is rolled twice. What is the probability that the face 5 turned up on first try given that the sum of the two faces is 9? 8 Z7 }1 S l5 V P(sum of faces is 9)=4/36=1/9. + J) d' p9 e9 R/ g5 Q7 O) I; K P(face 5 turns up on the first try and sum is 9)=(1/6)*(1/6)=1/36. / A, `$ U9 D5 a8 X U+ l P(face 5 turned up on first try given sum is 9)=(1/36)*(1/9)=1/4 " y( i$ L$ t; l$ x Remember:6 n: f1 T! f$ R! }
If P(AIB)=P(A),then two events A and B are independent, that is occurrence of one does not influence the other
发表于 2012-8-15 12:55:17
