Multiplication rule: dependent events, Mathematics

Multiplication Rule: Dependent Events

The joint probability of two events A and B which are dependent is equal to the probability of A multiplied by the probability of B given that A has occurred.

P(A and B)        =P(A) P(B|A)

or P(B and A)    =P(B) . P(A|B)

This formula is derived from the formula of conditional probability of dependent events.

P(B|A) = 1821_multiplication rule.png

Þ P(A and B) = P(B|A).P(A)

Example 

A study of an insurance company shows that the probability of an employee being absent on any given day P(A) is 0.1. Given that an employee is absent, the probability of that employee being absent a second day in succession P(B|A) is 0.4. Events A and B are dependent events because B cannot occur unless event A has occurred. The probability of an employee being absent on two successive days

P(A and B)      =P(A) . P(B|A)

                     =(0.1) (0.4) = 0.04

Thus, the probability of an employee being absent on two successive days is 0.04 or 4% of the time.

Joint probability of several dependent events is equal to the product of the probabilities of occurrence of the preceding outcomes in the sequence.

P(A and B and C...) = P(A) P(B|A) P(C|A and B) .... 

Posted Date: 9/14/2012 4:45:26 AM | Location : United States







Related Discussions:- Multiplication rule: dependent events, Assignment Help, Ask Question on Multiplication rule: dependent events, Get Answer, Expert's Help, Multiplication rule: dependent events Discussions

Write discussion on Multiplication rule: dependent events
Your posts are moderated
Related Questions
ther are 162 student in a school.20 of them are girls .how many are boy


Explain Equivalent Fractions ? Two fractions can look different and still be equal. Different fractions that represent the same amount are called equivalent fractions. Ar

The students at Norton School were asked to name their favorite type of pet. Of the 430 students surveyed, 258 said in that their favorite type of pet was a dog. Assume that only 1

Factoring polynomials is probably the most important topic. We already learn factor of polynomial .If you can't factor the polynomial then you won't be able to even start the probl

Find out the Greatest Common Factor? The largest number that is a common factor of two numbers (that is, both numbers share the same factor) is called the greatest common facto

Example of 3-D Coordinate System Example: Graph x = 3 in R, R 2 and R 3 .   Solution In R we consist of a single coordinate system and thus x=3 is a point in a 1-D co

interestind topic in operation research for doing project for msc mathematics

Q. How to Add Mixed Numbers? Ans. If you have to add mixed numbers, you might try this method first: First rewrite the mixed number as a whole number plus a fracti

solve the equation 540+115 using the NOWA method