chapter 4 notes

chapter 4 notes - Notes for Chapter 4 from Stat 225 Section...

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Notes for Chapter 4 from Stat 225 Section 4.1 Conditional Probability Conditional Probability- Let A and B be events. The probability that event B occurs given that event A occurs is called a conditional probability, and it is denoted by: ) ( ( ) P B P B P A (Α ∩ | Α) = . The event on the right side is the “given” event. It is read probability of B given A. As long as P(A)>0, you can use the above formula. This works as long as you know the 2 probabilities on the right side. This is very useful in Venn Diagram problems. However, for simpler cases you can also find it by the following: ( P B Ν(Α ∩Β) | Α) = Ν(Α) This second equation can be used for “simple” examples (examples where is small and all outcomes are known and have equal probability). Some examples where this would work would be flipping a (fair) coin repeatedly, or rolling a (fair) dice 1 or 2 times, etc. ( ) N Ω Section 4.2 General Multiplication Rule and Law of Total Probability General Multiplication Rule: ( ) ( )* ( P A B P A P B = | Α) 1

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