102420: [AtCoder]ABC242 A - T-shirt
Description
Score : $100$ points
Problem Statement
In a certain programming contest, T-shirts are awarded to participants according to the following rules.
- All participants who ranked $A$-th or higher get a T-shirt.
- Additionally, from the participants who ranked between $(A+1)$-th and $B$-th (inclusive), $C$ participants chosen uniformly at random get a T-shirt.
There were $1000$ participants in this contest, and all of them got different ranks.
Iroha-chan, who participated in this contest, ranked $X$-th.
Find the probability that she gets a T-shirt.
Constraints
- All values in input are integers.
- $1 \le A < B \le 1000$
- $1 \le C \le B-A$
- $1 \le X \le 1000$
Input
Input is given from Standard Input in the following format:
$A$ $B$ $C$ $X$
Output
Print the answer. Your output will be considered correct if the absolute or relative error from the judge's answer is at most $10^{−6}$.
Sample Input 1
30 500 20 103
Sample Output 1
0.042553191489
Iroha-chan ranked $103$-rd.
She will get a T-shirt if she is among the $20$ participants chosen uniformly at random from the $470$ participants who ranked between $31$-st and $500$-th, which happens with probability $\frac{20}{470}=0.04255319\dots$.
Sample Input 2
50 500 100 1
Sample Output 2
1.000000000000
Iroha-chan ranked $1$-st. This time, she is guaranteed to get a T-shirt.
Sample Input 3
1 2 1 1000
Sample Output 3
0.000000000000
Iroha-chan ranked $1000$-th. This time, she will never get a T-shirt.
Input
题意翻译
共 $1000$ 位选手参加比赛，前 $A$ 位选手必得奖，第 $A+1$ 到 $B$ 名随机选 $C$ 位选手得奖，在每个人排名都不同的情况下第 $X$ 名得到奖的概率是多少。 答案误差在 $10^{-6}$ 一下判为正确。 Translated by ShanCreeper.Output
分数：$100$分
问题描述
在某次编程竞赛中，根据以下规则向参赛者颁发T恤。
- 排名在第$A$名或以上的所有参赛者都将获得T恤。
- 此外，从排名在第$(A+1)$名到第$B$名（含）的参赛者中，随机均匀选择$C$名参赛者获得T恤。
这次比赛有$1000$名参赛者，所有人都得到了不同的排名。
参加了这次比赛的いろは酱排名为第$X$名。
求她获得T恤的概率。
限制条件
- 输入中的所有值都是整数。
- $1 \le A < B \le 1000$
- $1 \le C \le B-A$
- $1 \le X \le 1000$
输入
输入数据从标准输入按以下格式给出：
$A$ $B$ $C$ $X$
输出
输出答案。 只要你的输出与评判答案之间的绝对误差或相对误差不超过$10^{−6}$，就会被认为是正确的。
样例输入1
30 500 20 103
样例输出1
0.042553191489
いろは酱排名为第$103$名。
如果她是排名在第$31$名到第$500$名之间的$470$名参赛者中被随机均匀选择的$20$名参赛者之一，那么她将获得T恤，这种情况发生的概率为$\frac{20}{470}=0.04255319\dots$。
样例输入2
50 500 100 1
样例输出2
1.000000000000
いろは酱排名为第$1$名。这次，她肯定会获得T恤。
样例输入3
1 2 1 1000
样例输出3
0.000000000000
いろは酱排名为第$1000$名。这次，她永远不会获得T恤。