Multiplication rule: dependent events, Mathematics

Assignment Help:

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) .... 


Related Discussions:- Multiplication rule: dependent events

Coefficient of determination, Coefficient of Determination It refers t...

Coefficient of Determination It refers to the ratio of the explained variation to the total variation and is utilized to measure the strength of the linear relationship. The s

Integrals involving roots - integration techniques, Integrals Involving Roo...

Integrals Involving Roots - Integration Techniques In this part we're going to look at an integration method that can be helpful for some integrals with roots in them. We hav

Profit and loss, a man buy car at rs.50 and sells it at gain of 14% find ...

a man buy car at rs.50 and sells it at gain of 14% find the sp

Integration, Awhat is the meaning and application sk question #Minimum 100 ...

Awhat is the meaning and application sk question #Minimum 100 words accepted#

LINEAR EQUATIONS, SOLVE THE inequation 0>-5 -X AND X Belongs TO R .Represen...

SOLVE THE inequation 0>-5 -X AND X Belongs TO R .Represent THE SOLUTION SET ON THE NUMBER LINE

Marketing, In a 2500 word report do the market analysis of China. Under thi...

In a 2500 word report do the market analysis of China. Under this you have to explain: - What are the advantages and disadvantages for foreign company to set up its business cent

Polar coordinates - parametric equations & polar coordinates, Polar Coordin...

Polar Coordinates Till this point we've dealt completely with the Cartesian (or Rectangular, or x-y) coordinate system.  Though, as we will see, this is not all time the easie

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd