[機統] 一題機率的問題

[eric80520 (freejustice)]

完整題目是

Electric current is transmitted from point A to point B provided at

least one of the circuits #1 through #n below is closed. If the circuits

closed independently of each other and with respective probabilities

p_i, i=1,...,n, determinethe probability that:

   i) Exactly one circuit is closed;
  ii) At least one circuit is closed;
 iii) Exactly m circuits are closed for 0 <= m <= n;
  iv) At least m circuits are closed with m as in part (iii);
   v) What do parts (i)-(v) become for p_1=p_2=‧‧‧=p_n=p, say?

大概的意思是一個電流從A到B至少要有一條電路是通路(closed)

現在有n條電路 各自closed的機率是p_1到p_n

上面的意思應該對吧 我不知道有沒有誤解題目的意思

i)的答案我算是
                  n
                 Σ p_i(1-p_1)...(1-p_i-1)(1-p_i+1)...(1-p_n)
                 i=1
  不知道對不對

ii)應該是1-(1-p_1)(1-p_2)...(1-p_n)

iii) (iv) 就不太會了 可以教我嗎？ 謝謝


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推 jacky7987   :第三個是剛好m條(所以就C(n,m)然後類似)
→ jacky7987   :第四個是至少m條(看你要用扣的還是加的)