# The population of a particular country consists of three ## Problem 45E Chapter 2

Probability and Statistics for Engineering and the Sciences | 9th Edition

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Problem 45E

The population of a particular country consists of three ethnic groups. Each individual belongs to one of the four major blood groups. The accompanying ?joint probability table ?gives the proportions of individuals in the various ethnic group–blood group combinations. Suppose that an individual is randomly selected from the population, and define events by A = { type A selected}, B = { type B selected}, and C = { ethnic group 3 selected}. a. Calculate ?P?(?A??? ?), andP(A ?C) . b. Calculate both P(A|C) and P(C|A) , and explain in context what each of these probabilities represents. c.If the selected individual does not have type B blood, what is the probability that he or she is from ethnic group 1?

Step-by-Step Solution:

Solution : Step 1: Here population of a particular country consists of three ethnic groups. And each one of them belong to one of the four major blood group. And also it is defined as the events A = { type A selected}, B = { type B selected}, and C = { ethnic group 3 selected}. Step 2 : a) we have to find P(A), P(C), and P(A C) here the corresponding joining probability is given as From the probability table it we can find directly that the P(A)= P( type A selected) =0.106+ 0.141+ 0.200= 0.447 P(C)= P(ethnic group 3 is selected)= .215+.200+.065+.020 =0.5 P(AC)=P( individuals from type A or from ethnic group 3 is selected) = P(A)+ P(C)-P(AC) We know that P(AC)= P(individuals having blood group A and belong to ethnic group 3 is selected)= .200 So p(AC)= 0.447+0.5- .200 = 0.747 Step 3: b) P(AC) 1)We know that P (A/C ) = P(C) So P(AC) = 0.200 P(C)= 0.5 P(A/C)= 0.2/0.5 = 0.4 2) Here P(C/A )= P(AC) P(A) (AC) = 0.200 P(A)= 0.447 =. 0.447 P(A/C) represent the probability that select individuals belong to blood group A that already belong to ethnic group 3. P(C/A) represent the probability that select individuals belong to the ethnic group that already belong to blood group A.

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##### ISBN: 9780321629111

Since the solution to 45E from 2 chapter was answered, more than 1204 students have viewed the full step-by-step answer. Probability and Statistics for Engineering and the Sciences was written by and is associated to the ISBN: 9780321629111. This full solution covers the following key subjects: selected, ethnic, Group, Blood, type. This expansive textbook survival guide covers 18 chapters, and 1582 solutions. This textbook survival guide was created for the textbook: Probability and Statistics for Engineering and the Sciences, edition: 9. The full step-by-step solution to problem: 45E from chapter: 2 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM. The answer to “The population of a particular country consists of three ethnic groups. Each individual belongs to one of the four major blood groups. The accompanying ?joint probability table ?gives the proportions of individuals in the various ethnic group–blood group combinations. Suppose that an individual is randomly selected from the population, and define events by A = { type A selected}, B = { type B selected}, and C = { ethnic group 3 selected}. a. Calculate ?P?(?A??? ?), andP(A ?C) . b. Calculate both P(A|C) and P(C|A) , and explain in context what each of these probabilities represents. c.If the selected individual does not have type B blood, what is the probability that he or she is from ethnic group 1?” is broken down into a number of easy to follow steps, and 120 words.

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