probility

2014-09-29 12:36 am

In this exercise you will solve the following problem:
If you roll eight dice, what is the probability that each of the numbers 1
through 6 appears on top at least once?
For 1 ≦ i ≦ 6, let Ei be the event that number i doesn't show up on any of
the dice.(a) Write a formula for P(Ei).

(b) Let k ≦ 6 and 1 ≦ i1 < i2 <...< ik ≦ 6.
Write a formula for P(Ei1 ∩Ei2 ∩...∩ Eik).
(c) Now use the inclusion-exclusion formula to write a formula for
P(E1 ∪ E2 ∪ ...∪E6).
This is the probability that some number doesn't appear when you
roll eight die.
Your formula should use the summation sign, powers and binomial
coecients.
(d) Using the solution to (c), write down the probability that each of the
numbers 1 through 6 appears on top at least once (a solution in the
form of a sum is ne; it is not necessary to actually calculate the value
of the sum).

回答 (2)

2014-09-29 1:12 am
✔ 最佳答案
可以,我可以用 inclusion-exclusion 教你做一次。

同時亦可以用 permutation 的做法。

我提供兩個方法給你參考。

2014-09-28 17:12:55 補充:
Please read:


圖片參考:https://s.yimg.com/rk/HA00430218/o/1187918784.png


2014-10-03 16:39:58 補充:
6C1 是指 {1, 2, 3, 4, 5, 6} 中選 1 個為沒擲出的點數。

6C2 是指 {1, 2, 3, 4, 5, 6} 中選 2 個為沒擲出的點數。

。。。
2014-10-03 5:48 pm
貓貓,
6C1 係點黎??

2014-10-03 09:50:59 補充:
6C1 係唔係計緊
AAA, BBB, CCC, DDD, EEE, FFF = 6combinations?


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