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Topic
An international workshop includes 12 students from the following countries: Vietnam, Japan, Singapore, India, Korea, Brazil, Canada, Spain, Germany, France, South Africa, Cameroon, each country has exactly 1 the student. Randomly select 2 students from the international student group to participate in BTC:
Calculate the probability of each of the following events:
a) A: “Two selected students are from Asia”
b) B: “Two selected students from Europe”
c) C: “Two selected students from America”
d) D: “Two selected students from Africa”
Solution method – See details
The probability of event A being a number, symbol \(P\left( A \right)\) is determined by the formula: \(P\left( A \right) = \frac{{n\left( A \right)}}{{n\left( \Omega \right)}}\), where \(n\left( A \right)\) and \(n\left( \Omega \right)\) denote the number of elements of set A and \(\Omega \) respectively.
Detailed explanation
Select 2 students from 12 students \( \Rightarrow \) convolution 2 of 12 \( \Rightarrow n\left( \Omega \right) = C_{12}^2 = 66\)
a) A: “Two selected students from Asia”:
There are 5 Asian countries: Vietnam, Japan, Singapore, India, HQ
\( \Rightarrow n\left( A \right) = C_5^2 = 10\)
\( \Rightarrow P\left( A \right) = \frac{{n\left( A \right)}}{{n\left( \Omega \right)}} = \frac{{10}}{{ 66}} = \frac{5}{{33}}\)
b) B: “Two selected students from Europe”: There are 3 European countries: Spain, Germany, France \( \Rightarrow n\left( B \right) = C_3^2 = 3\)
\( \Rightarrow P\left( B \right) = \frac{{n\left( B \right)}}{{n\left( \Omega \right)}} = \frac{3}{{66} } = \frac{1}{{22}}\)
c) C: “Two selected students from America”: There are 2 American countries: Brazil, Canada \( \Rightarrow n\left( C \right) = C_2^2 = 1\)
\( \Rightarrow P\left( C \right) = \frac{{n\left( C \right)}}{{n\left( \Omega \right)}} = \frac{1}{{66} }\)
d) D: “Two selected students from Africa”: There are 2 African countries: South Africa, Cameroon \( \Rightarrow n\left( D \right) = C_2^2 = 1\)
\( \Rightarrow P\left( D \right) = \frac{{n\left( D \right)}}{{n\left( \Omega \right)}} = \frac{1}{{66} }\)
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