Question

统计的概率（排列组合）问题 求大神指导

On a Piccadilly train platform, 20 passengers are waiting to get on the train, which has 4 carriages. The number of free seats Ni,i = 1,...,4 available in each carriage i has Binomial distribution Ni ∼ Bin(30,0.2), independently of each other.
(a) What is the distribution of the total number of available seats? Explain your answer carefully. [3] 答案：Bin(120,0.2).
(b) What is the probability that there are exactly 24 seats available in total (across all carriages)? [6] Hint: you may use a continuous approximation to the Binomial distribution.
答案：0.0908, but the exact number will depend on the approximation from the tables.
(c) What is the probability that the passengers will be able to sit together in 2 groups of 10 (i.e. that at least 2 carriages have at least 10 free seats), including the possibility that all 20 passengers sit in the same carriage? [6] Hint: again, you may use a continuous approximation.
答案：0.017, but the exact number will depend on the approximation from the tables.

Answer 1

(a)，5/150=1/30
(b)，5/100=1/20
(c)，(1/30)*(1/20)=1/600
(d)，150名学生每人都有相同的机会被两次点名，则被两次点名那位学生是郑某的概率是1/150.
c答案是49/600 d的答案是1/100