# Venn Diagram Word Question

• Jun 29th 2010, 09:39 AM
rooney
Venn Diagram Word Question
Rite I will supply what I think is the correct answer and if someone could confirm if this is correct or not I would be extremely grateful. Got a handful of these to do so obv need to know if im on rite track:

students reported the following facts: (a) 37% played football (b) 12% played basketball and football (c) 48% played neither basketball nor football.

Deduce the % which played basketball.

I worked it out to be 12% + 15% = 27%
• Jun 29th 2010, 10:16 AM
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Quote:

Originally Posted by rooney
Rite I will supply what I think is the correct answer and if someone could confirm if this is correct or not I would be extremely grateful. Got a handful of these to do so obv need to know if im on rite track:

students reported the following facts: (a) 37% played football (b) 12% played basketball and football (c) 48% played neither basketball nor football.

Deduce the % which played basketball.

I worked it out to be 12% + 15% = 27%

I get the same answer, via 52% - 25% = 27%.
• Jun 29th 2010, 01:51 PM
Soroban
[Hello, rooney!

Quote:

Students reported the following facts:
. . (a) 37% played football
. . (b) 12% played basketball and football
. . (c) 48% played neither basketball nor football.

Deduce the % which played basketball.

I worked it out to be 12% + 15% = 27% . . . . Yes!

Since 48% played neither sport,
. . then 52% played either Football or Basketball (or both).

I used the formula: .\$\displaystyle P(F \cup B) \;=\;P(F) + P(B) - P(F \cap B)\$

Substitute the known values: .\$\displaystyle 52\% \;=\;37\% + P(B) - 12\% \$

Therefore: .\$\displaystyle P(B) \:=\:27\%\$