请教几个math题目---望达人不吝赐教

zxy26071985UID: 2177051

97 GRE-SUB
NO.2:
What is the least upper bound of the set of all numbers A such that a polygon with area A can be inscribed in a semicircular region of radius 1?
a)4/5  b)2/sqrt(5)   c)1   d)pi/2   d)2
NO17
Alternatively a fair coin is tossed and a fair die is thrown, beginning with the coin. What is the probability that the coin will register a "head" before the die registers a "5" or a "6"?
a)1/3   b)1/2    c)3/5   d)2/3     e)3/4

[ 本帖最后由 zxy26071985 于 2007-11-1 00:29 编辑 ]

hlzhang431UID: 2297648

1. 最小上确界为区域面积pi/2;
2. 1/2

GOUjiangtaoUID: 2400143

2.  3/4

GOUjiangtaoUID: 2400143

2.  3/4

geniusvUID: 2389750

楼上正解
第一个是因为整个半圆可以用内切多边形任意逼近，所以上确界就是半圆面积
第二个是打字说不清楚反正是0.75

bill0511UID: 2372793

奇怪，我做出来也是1/2，我的是 1 - sum((1/3)^n), n from 1 to infinity, 所以是1/2。

bill0511UID: 2372793

为什么楼上几位做出来是3/4呢？

bill0511UID: 2372793

啊，我知道我那里做错了，应该是1 - 1/2*sum((1/3)^n), n from 1 to infinity， 这样就是3/4了。要细心啊。