Every class in a school has 400 pupils. Of them, 50 study business studies, 300 study French, and 270 study math. Everybody who studies math also studies French. Twenty take business and math courses. 35 pursue business and French studies. A pupil is chosen at random. Calculate the likelihood that the chosen student studies business studies or French but not math or science. Only use Venn diagrams. [Answer Limit: 125 words] [UKPSC 2012]
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To solve this problem using a Venn diagram:
Define the Sets:
ЁЭСА
M: Students studying Maths (270)
ЁЭР╣
F: Students studying French (300)
ЁЭР╡
B: Students studying Business Studies (50)
Given Data:
All Maths students also study French:
тИг
ЁЭСА
тИй
ЁЭР╣
тИг
=
270
тИгMтИйFтИг=270
Students studying both Maths and Business Studies:
тИг
ЁЭСА
тИй
ЁЭР╡
тИг
=
20
тИгMтИйBтИг=20
Students studying both French and Business Studies:
тИг
ЁЭР╣
тИй
ЁЭР╡
тИг
=
35
тИгFтИйBтИг=35
Calculate Intersections:
Students studying all three subjects:
тИг
ЁЭСА
тИй
ЁЭР╣
тИй
ЁЭР╡
тИг
=
20
тИгMтИйFтИйBтИг=20
Students studying only French and Business Studies:
тИг
ЁЭР╣
тИй
ЁЭР╡
тИг
тИТ
тИг
ЁЭСА
тИй
ЁЭР╣
тИй
ЁЭР╡
тИг
=
35
тИТ
20
=
15
тИгFтИйBтИгтИТтИгMтИйFтИйBтИг=35тИТ20=15
Students studying only French:
Total studying French:
300
тИТ
270
тИТ
15
=
15
300тИТ270тИТ15=15
Probability:
Students studying only French = 15
Total students = 400
ЁЭСГ
(
only┬аFrench
)
=
15
400
=
3
80
P(only┬аFrench)=
400
15
тАЛ
=
80
3
тАЛ
Thus, the probability that the selected student studies French but neither Maths nor Business Studies is
3
80
80
3
тАЛ
.