The table below shows the soft drink preferences or people in three age groups. (Round to threedecimal places)ColaRoot BeerLemonTotalUnder 21 year of age40252085Between 21 and 4035203085Over 40 years of age20303585Total75a) If one nerson is randomly selected, find the probability that the person is over 40 years of9585255age.b) If one person is randomly selected, find the probability that the person is over 40 anddrinks cola.c) If one person is randomly selected, find the probability that the person is over 40 or drinkscolad) If two people are randomly selected without replacement, find the probability that bothpeople are between 21 and 40

GivenThe data is as follows:ColaRoot BeerLemonTotalUnder 21 year of age40252085Between 21 and…

Answered: The table below shows the soft drink…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

The table below shows the soft drink preferences or people in three age groups. (Round to three
decimal places)
Cola
Root Beer
Lemon
Total
Under 21 year of age
40
25
20
85
Between 21 and 40
35
20
30
85
Over 40 years of age
20
30
35
85
Total
75
a) If one nerson is randomly selected, find the probability that the person is over 40 years of
95
85
255
age.
b) If one person is randomly selected, find the probability that the person is over 40 and
drinks cola.
c) If one person is randomly selected, find the probability that the person is over 40 or drinks
cola
d) If two people are randomly selected without replacement, find the probability that both
people are between 21 and 40

Expert Solution

Step 1: Step 1

Given

The data is as follows:

	Cola	Root Beer	Lemon	Total
Under 21 year of age	40	25	20	85
Between 21 and 40	35	20	30	85
Over 40 years of age	20	30	35	85
Total	95	75	85	255

Step 2: Step 2

No. of people over age of 40 years = 85

Total no. of people = 255

$table row cell P r o b a b i l i t y end cell equals cell fraction numerator N o. space o f space f a v o u r a b l e space o u t c o m e s over denominator T o t a l space n o. space o f space o u t space c o m e s end fraction end cell row blank equals cell 85 over 255 end cell row blank equals cell 0.33333 end cell row blank almost equal to cell 0.333 end cell end table$

Hence, the prob. of selecting a person over age of 40 is 0.333.

Step 3: Step 3

No. of people over 40 and drinks cola = 20

Total no. of people = 255

$table row cell P r o b a b i l i t y end cell equals cell fraction numerator N o. space o f space f a v o u r a b l e space o u t c o m e s over denominator T o t a l space n o. space o f space o u t space c o m e s end fraction end cell row blank equals cell 20 over 255 end cell row blank equals cell 0.078431 end cell row blank almost equal to cell 0.078 end cell end table$

Hence, the prob. of selecting a person who is over 40 and drinks cola is 0.078.