Answer:
Step-by-step explanation:
The Venn diagram representing the situation is shown in the attached photo.
G represents the set of people that use the gym.
P represents the set of people that use the swimming pool.
T represents the set of people that use the track.
Since 1 person uses the 3 facilities, it means that
Number of persons that use gym and pool only is 15 - 1 = 14
Number of persons that use pool and track only is 14 - 1 = 13
Number of persons that use gym and track only is 10 - 1 = 9
Number of persons that use gym only is
65 - (14 + 1 + 9) = 41
Number of persons that use pool only is
51 - (14 + 1 + 13) = 23
Number of persons that use track only is
44 - (9 + 1 + 13) = 21
N represents the number of people that use none of the facilities. Since there are 130 people in a sports centre, it means that
41 + 23 + 21 + 9 + 14 + 13 + 1 + N = 130
122 + N = 130
N = 130 - 122
N = 8
Therefore, the probability that a person doesn't use any facilities is
8/130 = 0.062
[tex]\frac{4}{65}[/tex] is the required probability.
A set is an unorganized well-defined collection of similar types of objects.
Eg : {1,2,3,4,5} or {Science, Maths, English}
Given:-
Total people (n) = 130
People using gym (G) = 65
People using swimming pool (P) = 51
People using track (T) = 44
(Gym U pool) = 15
(pool U track) = 14
(Gym U track) = 10
(Gym U track U pool) = 1
Using venn diagram :
Total participating people are 41 + 23 + 21 + 14 + 9 + 13 + 1 = 122
since total people are 130, non participants are 130 - 122 = 8
Probability of an event = [tex]\frac{favourable}{total}[/tex] = [tex]\frac{8}{130} = \frac{4}{65}[/tex]
Thus, the probability that a random person doesn't uses any facility is [tex]\frac{4}{65}[/tex]
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