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

What is deductive reasoning, What is Deductive Reasoning ? Geometry is...

What is Deductive Reasoning ? Geometry is based on a deductive structure -- a system of thought in which conclusions are justified by means of previously assumed or proved sta

Find k to three decimal places, The population of a city is observed as gro...

The population of a city is observed as growing exponentially according to the function P(t) = P0 e kt , where the population doubled in the first 50 years. (a) Find k to three

Multiplication example, Example  Multiply 3x 5 + 4x 3 + 2x - 1 ...

Example  Multiply 3x 5 + 4x 3 + 2x - 1 and x 4 + 2x 2 + 4. The product is given by 3x 5 . (x 4 + 2x 2 + 4) + 4x 3 . (x 4 + 2x 2 + 4) + 2x .

Differential equation, Cos(x+y)+sin(x+y)=dy/dx(solve this differential equa...

Cos(x+y)+sin(x+y)=dy/dx(solve this differential equation)

Shares and dividents., how much money will required to buy 200,rupees 25 sh...

how much money will required to buy 200,rupees 25 shares at premium of rupees 2

Mr, i needed help with algebra

i needed help with algebra

Case study, considring the concept of product life cycle,where would you pu...

considring the concept of product life cycle,where would you put viedo games in thier life cycle?

Give an example of divisibility, Give an example of Divisibility? If yo...

Give an example of Divisibility? If you can divide one number by another without getting a remainder, we say that the first number is divisible by the second. For instance, the

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