SOLUTION: 1. Suppose in a group of 500 men, it is found that 210 like to jog, 258 play badminton, 216 maintain a healthy eating habit, 122 jog and play badminton, 83 maintain a healthy eat

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Question 1194257: 1. Suppose in a group of 500 men, it is found that 210 like to jog, 258 play badminton, 216
maintain a healthy eating habit, 122 jog and play badminton, 83 maintain a healthy eating habit
and play badminton, 97 jog and practice healthy eating habits and 52 involve all three practices,
find the probability that the man:
a. Jog but does not eat healthily
b. Eats healthily and plays badminton but does not jog.
c. Does not jog or eat healthily
(show the above given in Venn Diagram)

Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
1. Suppose in a group of 500 men, it is found that 210 like to jog, 258 play badminton, 216
maintain a healthy eating habit, 122 jog and play badminton, 83 maintain a healthy eating habit
and play badminton, 97 jog and practice healthy eating habits and 52 involve all three practices,
find the probability that the man:
a. Jog but does not eat healthily
b. Eats healthily and plays badminton but does not jog.
c. Does not jog or eat healthily
(show the above given in Venn Diagram)
~~~~~~~~~~~~~~~~~


            In this my post,  I will answer questions  (a)  and  (b),  ONLY.


a. Jog but does not eat healthily


This set "Jog but does not eat healthily" is the set of those who like jog (210 persons, given) 
 the intersection of those who jog  AND  eat healthy (i.e. minus 97).


    So, the  ANSWER to question (a)  is  210 - 97 = 113.

b. Eats healthily and plays badminton but does not jog.


This set "Eats healthily and plays badminton but does not jog" is the set of those who maintain a healthy eating habit
and play badminton (83 persons, given)  the triple intersection of those who involve all three practices 
(i.e. minus 52).


    So, the  ANSWER to question (b)  is  83 - 52 = 31.



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


J = jog
B = play badminton
H = eat healthily

The categories below indicate which of the three things individuals do -- e.g., "BH" means plays badminton and eats healthily but does not jog.

JBH: 52 (given)

JB: 122 (given) - 52 = 60
JH: 97 (given) - 52 = 45
BH: 83 (given) - 52 = 31

J: 210 (given) - (60+45+52) = 53
B: 258 (given) - (60+31+52) = 115
H: 216 (given) - (45+31+52) = 88

ANSWERS:

a. Jog but does not eat healthily:
J + JB = 53+60 = 113

b. Eats healthily and plays badminton but does not jog:
BH = 31

c. Does not jog or eat healthily:
B = 115
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