A class has 12 boys and 8 girls. Two students are chosen at random to represent the class. What is the probability that both chosen students are girls?
14/95
16/95
2/5
7/38
Show the answer and explanation
Correct answer
A. 14/95
Principle or equation
Classical probability: P(both girls) = (number of ways to choose 2 girls) / (number of ways to choose 2 students).
Why this answer is correct
Total students = 20. Number of ways to choose 2 girls = C(8,2) = 28. Number of ways to choose 2 students = C(20,2) = 190. Probability = 28/190 = 14/95.
Example
If there were 5 boys and 5 girls, P(both girls) = C(5,2)/C(10,2) = 10/45 = 2/9.
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