Theory question 106
ProbabilityThere are 6 boys and 8 girls in a class. If five students are selected from the class, find the probability that more girls than boys are selected.
Show the model answer
Model answer
Total selections: ¹⁴C₅ = 2002.
3 girls, 2 boys: ⁸C₃ × ⁶C₂ = 56 × 15 = 840; 4 girls, 1 boy: 70 × 6 = 420; 5 girls: ⁸C₅ = 56.
Favourable = 1316. P = 1316/2002 = 94/143 ≈ 0.657.
Explanation
'More girls than boys' in a group of 5 means 3, 4 or 5 girls.