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

What is a marketing mix, Problem 1: (i) What is a marketing mix? (ii...

Problem 1: (i) What is a marketing mix? (ii) Will the nature and composition of the marketing mix be the same for all products at the same stage in the product-market life c

Market segmentation, one primary segmets and two secondary segments

one primary segmets and two secondary segments

COMMNICATIONS, #1 What is the most important benefit of listening?

#1 What is the most important benefit of listening?

Describe the kuleshov effect, Question 1 Write short notes on any 5 of ...

Question 1 Write short notes on any 5 of the following concepts: (i) Close Up (ii) Wide Shot (iii) Pan (iv) Tilt (v) Zoom (vi) Subjective Camera movement (vii)

Dysons trade and customer target markets, Question: Dyson intends to la...

Question: Dyson intends to launch its brand in Mauritius with the ambition to subsequently go regional. a. You work for a marketing consulting firm and have been asked to

Explain about the marketing information system, Explain about the Marketing...

Explain about the Marketing Information System. As demonstrated in the given figure: Figure: Marketing Information System Marketing information System means the

International marketing., Companies entering emerging markets for the first...

Companies entering emerging markets for the first time must exercise particular care in choosing a channel intermediary. Usually a local distributor is required. What are some of t

Significance of problem recognition in decision making, What is the signifi...

What is the significance of problem recognition in decision making process? Problem Recognition: As any other decision-making process, this is the first stage of the organ

Assignment, consumer mind is a black box discuss

consumer mind is a black box discuss

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