Theory question 105
ProbabilityFive students are to be selected from a large population. If 60% of them are boys and the rest are girls, find the probability that:
(a) exactly 3 of them are boys;
(b) at least 3 of them are girls.
Show the model answer
Model answer
P(boy) = 3/5, P(girl) = 2/5 (binomial, n = 5)
(a) 5C3(3/5)3(2/5)2 = 10 × 27/125 × 4/25 = 216/625 (0.3456)
(b) P(3, 4 or 5 girls) = 5C3(2/5)3(3/5)2 + 5C4(2/5)4(3/5) + (2/5)5
= 720/3125 + 240/3125 + 32/3125 = 992/3125 (≈ 0.317)
Explanation
Each selection is a binomial trial with p = 0.6 for a boy.