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

.fractions, what is the difference between North America''s part of the tot...

what is the difference between North America''s part of the total population and Africa''s part

Fact - undetermined coefficients, Here, let's take a look at sums of the fu...

Here, let's take a look at sums of the fundamental components and/or products of the fundamental components. To do this we'll require the following fact. Fact- Undetermined Co

Positive skewness-measure of central tendency, Positive Skewness - It ...

Positive Skewness - It is the tendency of a described frequency curve leaning towards the left. In a positively skewed distribution, the long tail extended to the right. In

Illustrate field properties of numbers, Q. Illustrate Field Properties of N...

Q. Illustrate Field Properties of Numbers? Ans. What the  associative law of addition  states is this: for any numbers a, b, and c,

Determine the area of the book jacket, A publishing company is creating a b...

A publishing company is creating a book jacket for a newly published textbook. Determine the area of the book jacket, given that the front cover is 8 in wide by 11 in high, the bin

Marketing research, In pharmaceutical product research doctors visit the pl...

In pharmaceutical product research doctors visit the place to learn what

Calculate the throughput and link utilization, 4. Two hosts, one on East (h...

4. Two hosts, one on East (host A) and one on the west coast (host B) of the USA are exchanging data. Suppose A is sending a large file to B. The file is split into packets of size

Example of pythagorean theorem, Any 15 foot ladder is resting against the w...

Any 15 foot ladder is resting against the wall. The bottom is at first 10 feet away from the wall & is being pushed in the direction of the wall at a rate of 1 ft/sec. How rapid is

Why x and y are simplifying expressions, Why x and y are Simplifying Expres...

Why x and y are Simplifying Expressions? You're doing algebra now, and you know you're going to see x's and y's. But before we work with x's and y's, we'll explore why we use t

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