// CoinExample6.java
//
// Author: Rahul Simha
// Feb, 2008.
//
// Pr[2nd is heads], Pr[2nd heads | 1st heads]

public class CoinExample6 {

    public static void main (String[] argv)
    {
	double numTrials = 1000000;

	double numSuccesses = 0;                   // #times C2 occurs.
        double numFirstHeads = 0;                  // #times C1 occurs.
        double numBothHeads = 0;                   // #times both are heads.

	for (int n=0; n<numTrials; n++) {
            //BizarreCoin coin = new BizarreCoin ();
            Coin coin = new Coin ();

	    int c1 = coin.flip ();            
	    int c2 = coin.flip ();

            if (c2 == 1) {
		numSuccesses ++;
            }
            
            if (c1 == 1) {
                numFirstHeads ++;
                if (c2 == 1) {
                    numBothHeads ++;
                }
            }
	}

        double prob1 = numSuccesses / numTrials;
        double prob2 = numBothHeads / numFirstHeads;

	System.out.println ("Pr[c2=1]=" + prob1 + "  Pr[c2=1|c1=1]=" + prob2);
    }
 
}