Answered: 4. An airline offers two types of…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

4. An airline offers two types of economic classes (a and b) on its flights and a class Executive In a certain flight, 25 people travel in economic class A of the which 15 are ladies; and 20 people in the economic class B of which 10 are ladies. The captain of the flight makes a person at random to the executive class. Yeah We know that this person is a lady, what is the probability of being of the Economic class A?

Expert Solution

Step 1: We use Bayes Theorem

There are 2 Economic classes A and B . Probability of choosing these classes are :

P(A)=P(B)= 1/2

Let D be the event that denotes ladies,then

P(D|A) = 15/25 = 0.6 : Prob that the lady is in Class A

P(D|B) = 10/20 = 0.5 : Prob that the lady is in class B

Then we have to find

P(A|D) = $fraction numerator P left parenthesis A right parenthesis. P left parenthesis D vertical line A right parenthesis over denominator P left parenthesis A right parenthesis. P left parenthesis D vertical line A right parenthesis plus P left parenthesis B right parenthesis. P left parenthesis D vertical line B right parenthesis end fraction equals fraction numerator 0.5 x.6 over denominator 0.5 x 0.6 plus 0.5 x 0.5 end fraction equals fraction numerator 0.6 over denominator 0.6 plus 0.5 end fraction equals fraction numerator 0.6 over denominator 1.1 end fraction$ =0.5455

using Bayes Theorm