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) = 

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) .... 

Posted Date: 9/14/2012 4:45:26 AM | Location : United States

Ask an Expert

Related Discussions:- Multiplication rule: dependent events, Assignment Help, Ask Question on Multiplication rule: dependent events, Get Answer, Expert's Help, Multiplication rule: dependent events Discussions

Write discussion on Multiplication rule: dependent events
Your posts are moderated

Write your message here..

Related Questions

Find out the volume of the solid -x = (y - 2)2, Find out the volume of th... Find out the volume of the solid obtained by rotating the region bounded by x =  (y - 2) 2 and  y = x around the line y = -1. Solution : We have to first get the intersection

Binomial expansion, Expand (1- 1/2x -x^2)^9 Expand (1- 1/2x -x^2)^9

Tent originally sold for $2 what is the percent of discount, A tent origina... A tent originally sold for $260 and has been marked down to $208. What is the percent of discount? Find out the number of dollars off. $260 - $208 = $52. Further, determine wha

Produce the individual answers and the insights in maths, It is difficult t... It is difficult to produce the individual answers and the insights that they were providing. But, let's look at some broad patterns that we found, which are similar to those that o

Find the constant rate of 0.01 , Two people are 50 feet separately.  One of... Two people are 50 feet separately.  One of them begin walking north at rate so that the angle illustrated in the diagram below is changing at constant rate of 0.01 rad/min. At what

Normal distribution to approximate binomial distribution, Survey 83% of com... Survey 83% of community for a park. Randomly select 21 people if they do or do not want a park. Can you use normal distribution to approximate binomial distribution?If so find mean

Hi, how do you find the distance between the sun and earth how do you find the distance between the sun and earth

Using two variables, Leo works at the Bagel Shop after school and on Saturd... Leo works at the Bagel Shop after school and on Saturdays. He is paid $4.00 per hour after school and $5.00 per hour on Saturday. Last week Leo worked a total of 12 hours and made

Unipolar and bipolar boolean inputs, A 4-input Neuron has weights (1,-1,  0... A 4-input Neuron has weights (1,-1,  0,  0.5.Calculate the network output when the following input vectors are applied. For calculation assume: a. f(net) = unipolar bina

Solve the equation for x, Solve the equation for x and check each solution.... Solve the equation for x and check each solution. 2/(x+3) -3/(4-x) = 2x-2/(x 2 -x-12)