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

Please solve this question, The number of integral pairs (x,y) satisfying t...

The number of integral pairs (x,y) satisfying the equation x^2=y^2+1294 is a)2 b)3 c)4 d)None of these

Explain how to distribute simplifying expressions, Explain How to Distribut...

Explain How to Distribute simplifying expressions? The distributive law states that for all numbers a, b, and c, a(b + c)= ab + ac What does this mean in plain language?

Compute the break-even quantities, The revenue and cost functions for produ...

The revenue and cost functions for producing and selling quantity x for a certain production facility are given below. R(x) = 16x - x 2 C(x) = 20 + 4x a)  Determine the p

Factoring polynomials, Factoring polynomials is probably the most important...

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

Derivative problem, we know that derivative of x 2 =2x. now we can write x...

we know that derivative of x 2 =2x. now we can write x 2 as x+x+x....(x times) then if we take defferentiation we get 1+1+1+.....(x times) now adding we get x . then which is wro

Congruences, Suppose m be a positive integer, then the two integer a and b ...

Suppose m be a positive integer, then the two integer a and b called congurent modulo m ' if a - b is divisible by m i.e.  a - b = m where is an positive integer. The congru

Simple random sampling, Simple Random Sampling It refers to the samplin...

Simple Random Sampling It refers to the sampling technique whether each and every item of the population is described an equal chance of being included in the sample. Because s

Determine whether the following numbers are odd or even, Determine whether ...

Determine whether the following numbers are odd or even: Examples: Determine whether the following numbers are odd or even:  364, 1068, & 257. Solution: 1.

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