Sports club has a membership of 800 and operates 26 baseball fields and 24 soccer fields. Before deciding whether to accept new members, the club council would
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1. User Answers oladayoademosu
The percentage of the 800 use both the soccer and baseball fields is 34 %.
Let S = set of people that use soccer field and B = set of people that use base ball field and B U S represent the universal set.
Since 62% use the baseball field regularly, P(B) = 64 %.
Also, 64% regularly use the soccer field, P(S) = 64 % and 3% do not regularly use either of these fields. Since this is a complement of the universal set, (B U S)'. So, P(B ∪ S)' = 3 %.
Since P(B ∪ S) + P(B ∪ S)' = 100 %
P(B ∪ S) = 100 %  P(B ∪ S)'
= 100 %  3 %
= 97 %
Now, from set theory,
P(B ∪ S) = P(B) + P(S)  P(B ∩ S)
where P(B ∩ S) = percentage that use both the soccer and baseball fields.
So, P(B ∩ S) = P(B) + P(S)  P(B ∪ S)
Substituting the values of the variables into the equation, we have
P(B ∩ S) = P(B) + P(S)  P(B ∪ S)
P(B ∩ S) = 64 % + 62 %  97 %
P(B ∩ S) = 126 %  97 %
P(B ∩ S) = 34 %
So, the percentage of the 800 use both the soccer and baseball fields is 34 %.
Learn more about set theory here:
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