Chapter3.6-3.7_revised lecture notes

# Chapter3.6-3.7_revised lecture notes - AMS 310 Chapter 3.6...

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AMS 310 Chapter 3.6- 3.7 3.6. Conditional Probability Definition of conditional probability : If A and B are any events in S and P(B) is not equal to zero, the conditional probability of A given B is P A B P A B P B ( | ) ( ) ( ) . = EXAMPLE : What is the probability that the number of dots on a fair die is even given that the number of spots showing is 3 or less? Definition of independent events : The event A is independent of the event B if P(A|B)=P(A) .Equivalently ) | ( ) | ( B A P B A P = ) . EXAMPLE : Suppose P(A and B) =1/8 and P(B) =1/6 and P(A)=1/2. Are A and B independent? Suppose A and B are independent. Then what is the value of P(A B)? Theorem 3.8. General multiplication rule of probability . If A and B are any events in S , then P(A B) = P(A|B)P(B) =P(B|A)P(A) for P(A), P(B) 0 EXAMPLE ( Using the General Multiplication Rule): We are told that we will get a job if we are in the top 10% of scores on two tests. Suppose however, the probability of being in the top 10% on test 2 given we are in the top 10% on test 1 equals 90%. What is the probability we will get the job?

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