美国以前有一个综艺节目。参赛者会看见三扇关闭了的门，其中一扇的后面有一辆汽车，选中后面有车的那扇门可赢得该汽车，另外两扇门后面则各藏有一只山羊。当参赛者选定了一扇门，但未去开启它的时候，节目主持人开启剩下两扇门的其中一扇，露出其中一只山羊。主持人其后会问参赛者要不要换另一扇仍然关上的门。问题是：换另一扇门会否增加参赛者赢得汽车的机会率？
以下为模拟三门问题的Java代码。
import java.util.Scanner;
import java.text.DecimalFormat;
import java.text.DecimalFormatSymbols;
//三门
class ThreeDoor {
String[] threeDoor = new String[3]; //三门
//设置门后的奖品
public void setPrize() {
int carPosition = (int)(Math.random()*100)%3;
threeDoor[0] = "Goat";
threeDoor[1] = "Goat";
threeDoor[2] = "Goat";
threeDoor[carPosition] = "Car";
}
}
//玩家
class Player {
int firstChoicePosition = 0; //首次选择的门
int lastChoicePosition = 0; //最终选择的门
//选择一个门
public void choiceDoor() {
firstChoicePosition = (int)(Math.random()*100)%3;
lastChoicePosition = firstChoicePosition;
}
//更换为另一个门
public void changeDoor(int firstGoatPosition) {
lastChoicePosition = 3 - firstChoicePosition - firstGoatPosition;
}
}
//主持人
class Presenter {
int firstGoatPosition = 0; //主持人打开的门
//打开后面为山羊的门
public void openFirstGoatPosition (String[] threeDoor,int playerFirstChoicePosition) {
if(threeDoor[playerFirstChoicePosition].equals("Car")) {
do {
firstGoatPosition = (int)(Math.random()*100)%3;
} while (firstGoatPosition == playerFirstChoicePosition);
} else {
for(int i=0;i<3;i++)
if(!threeDoor[i].equals("Car") && i!=playerFirstChoicePosition)
firstGoatPosition = i;
}
}
}
//计分牌
class Scorer {
int playCount = 0; //玩的总次数
int choiceCarCount = 0; //获得车的次数
int choiceGoatCount = 0; //获得山羊的次数
//计分
public void score(String[] threeDoor,int playLastChoicePosition) {
playCount++;
if(threeDoor[playLastChoicePosition].equals("Car"))
choiceCarCount++;
else
choiceGoatCount++;
}
//计算获得车的概率
public void statistics() {
DecimalFormat df = new DecimalFormat("##.00%");
System.out.println("Choice Goat Count: " + choiceGoatCount);
System.out.println("Choice Car Count: " + choiceCarCount);
System.out.println("Choice Car Rate : " + df.format((float)choiceCarCount/playCount));
}
}
//设置模式
class Moder {
String mode = ""; //模式，A：换门，B：不换门
int playTotalCount = 0; //玩的总次数
//设置模式
public void setMode() {
Scanner sc = new Scanner(System.in);
//设置选门模式
while(!mode.equals("A") && !mode.equals("B")) {
System.out.println("Plase input mode: A[Change] B[Don't Change]");
mode = sc.nextLine();
if(!mode.equals("A") && !mode.equals("B"))
System.out.println("Input Error, Input again.");
}
//设置玩的总次数
while(playTotalCount<=0) {
System.out.println("Plase input play total count: ");
try {
Scanner scCnt = new Scanner(System.in);
playTotalCount = scCnt.nextInt();
} catch(Exception e) {
playTotalCount = 0;
}
if(playTotalCount<=0)
System.out.println("Input Error, Input again.");
}
System.out.println();
}
//显示设置的模式
public void showMode() {
if(mode.equals("A"))
System.out.println("Mode: [Change]");
else
System.out.println("Mode: [Don't Change]");
System.out.println("Play Total Count: " + playTotalCount);
System.out.println();
}
}
//main程序
class ThreeDoorDemo {
public static void main(String[] args) {
ThreeDoor threeDoor = new ThreeDoor(); //三门
Player player = new Player(); //玩家
Presenter presenter = new Presenter(); //主持人
Scorer scorer = new Scorer(); //计分者
Moder moder = new Moder(); //设置模式者
moder.setMode(); //设置模式
moder.showMode(); //显示模式
//循环玩多次
for(int i=0; i<moder.playTotalCount; i++) {
threeDoor.setPrize(); //设置门后奖品
player.choiceDoor(); //玩家选择一个门
//主持人打开一扇是山羊的门
presenter.openFirstGoatPosition(threeDoor.threeDoor,player.firstChoicePosition);
if(moder.mode.equals("A"))
player.changeDoor(presenter.firstGoatPosition); //玩家换另外一扇门
//计分
scorer.score(threeDoor.threeDoor,player.lastChoicePosition);
}
scorer.statistics(); //统计获得汽车的概率
}
}
