主题：【原创】问道概率题 -- baiqi

Consider the tallest one amount the first 20 persons, and name him "X". let's call the shortest one the 1'st person, and the tallest one the 100'th person.

X is the x'th person. Obviously, x could be any number between 20 and 100.

Next, we will pick up an "Y", while we go through the original line. This Y is the y'th person in height. Apparently, the range of y is [x + 1, 100].

The question is:

What is the probability of y being 96 - 100?

The desired consequence is comprised by two events, event A and event B. Event A is the combination of the first 20 persons, and Event B is picking up a "good" person from the rest of the line. For example:

event A event B

------- -------

1) x = 20 96'th - 100'th got picked

2) x = 21 96'th - 100'th got picked

.

.

.

77) x = 96 97'th - 100'the got picked

.

.

The final answer should be the summation of the probability of each row. The probability of each row should be the multiple of the probabilities of event A and event B in that row.

The probability of event B in each row is comparatively easy. For instance, P(B) of row 1 should be 5 / (100 - 20).

The calculation of column A is complicated. Taking the first row as an example, the point is that the first 20 persons you encountered are indeed the first 20 persons regarding to their height. The order between these 20 persons is not important (any combination is allowed).

need some more work...