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

Assignment, how do mathematical ideas grow?

how do mathematical ideas grow?

Substitutions at bernoulli equations, In the prior section we looked at Ber...

In the prior section we looked at Bernoulli Equations and noticed that in order to solve them we required to use the substitution v = y 1-n . By using this substitution we were cap

Triangulos rectangulos y no rectangulos, el extremo de un poste que partió ...

el extremo de un poste que partió 8.45 metros de la base del poste y forma con el suelo un angulo de 40 grados 28 minutos.hallar la altura original del poste

Area, #What is an easy way to find the area of any figure

#What is an easy way to find the area of any figure

Lucy youth group increased $1, Lucy's youth group increased $1,569 for char...

Lucy's youth group increased $1,569 for charity. They decided to split the money evenly between 3 charities. How much will each charity receive? Divide the money raised through

Derivatives of exponential and logarithm functions, Derivatives of Exponent...

Derivatives of Exponential and Logarithm Functions : The next set of functions which we desire to take a look at are exponential & logarithm functions. The most common exponentia

Supply/demand, For the pair of supply-and-demand equations, where x represe...

For the pair of supply-and-demand equations, where x represents the quantity demanded in units of 1000 and p is the unit price in dollars, find the equilibrium quantity and the equ

Introducing counting, INTRODUCING COUNTING : From what you studied previou...

INTRODUCING COUNTING : From what you studied previous study, you know what it means to count. You would also agree that rote learning of number names does not always mean that the

Help, I really need help with 30 60 90 right triangles and my last tutor di...

I really need help with 30 60 90 right triangles and my last tutor did not make sense to me so can you please help

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