Conditional probability, math, Marketing Management

Assignment Help:

What is Conditional Probability?

Two events A and B are said to be dependent when B can occur only when A is known to have occurred (or vice versa). The probability attached to such an event is called the conditional probability and is denoted byP(A/B) or, in other words probability of A given that B has occurred.

If two events A and B are dependent, then the conditional probability of B given A is:

P(B/A) = P(AB)/P(A)

Proof: suppose a1 is the number of cases for the simultaneous happening of A and B out of a1 + a2 cases in which A can happen with or without happening of B.

∴ P(B/A) = a1/(a1 + a2) = (a1/n)/(a1 + a2)/n = P(AB)/P(A)

Similarly it can be shown that

P(A/B) = P[(AB)/P(B)]

The general rule of multiplication in its modified form in terms of conditional probability becomes:

P(A and B) = P(B) × P(A/B)

Or, P(A and B) = P(A) × P(B/A)

For three events A, B and C we have

P(ABC) = P(A) × P(B/A) × P(C/AB)


i.e. the probability of occurrence of A, B and C is equal to the probability of A, times of the probability of B given that A has occurred, times the probability of C given that both A and B have occurred.

Illustration: a bag contains 5 white and 3 black balls. Two balls are drawn at random one after the other without replacement. Find the probability that both balls drawn are black.

Solution: probability of drawing a black ball in the first attempt is

P(A) = 3/(5 + 3) = 3/8

Probability of drawing the second black ball given that the first ball drawn is black

P(B/A) = 2/(5 + 2) = 2/7

∴ The probability that both balls drawn are black is given by

P(AB) = P(A) × P(B/A) = 3/8 × 2/7 = 3/28  

Math Assignment Help


Related Discussions:- Conditional probability, math

Brand promotion, Can brand promotion technique benefit an organization by i...

Can brand promotion technique benefit an organization by increasing its sales or hitting competitive brands may leave a negative impression on the customers?

Assertive confrontation message to an employee, Question (a) When deli...

Question (a) When delivering an assertive confrontation message to an employee, you have to be careful not to become defensive or reactive if the employee becomes argumentati

Explain the strategic decision regarding packaging, Explain the strategic d...

Explain the strategic decision regarding packaging. Packaging Strategies: To control the packaging of product executives should make the given strategic decisions as given

Marketing strategy multi player, #questionThis week in the Music2Go Multi-P...

#questionThis week in the Music2Go Multi-Player you will be required to launch a New Product into one of the empty Market Segments (Sports or Youth). Part of this process will be t

Calculus, a) Use the simplified difference quotient method to find g''(x) f...

a) Use the simplified difference quotient method to find g''(x) for g(x)= (2)/(1+2x) b) Determine an equation for the tangent line to the graph of g in part a) at x=0 c) Give th

Explain the role of human resource accounting, Question: The recognitio...

Question: The recognition of human capital by modern businesses has led to the development of Human Resource Accounting (HRA). Required (a) Describe the following terms:

Describe the importance of television advertising, Question 1: The term...

Question 1: The term "Below the Line Media" refers to the non-commission paying advertising media like direct mail, sales literature, point of sale display material, exhibition

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