John Ferguson Lab 2

Answers.md

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+#John Ferguson    2/5/15
+##Dice Rolling Lab
+
+>**Question 1:** The probability of rolling a certain number is the number of possbile rolls that can sum to that number divided by the total number of possible rolls. What is the probability of rolling a 7? What is the probability of rolling a 2?
+
+**Answer 1:** The probability of rolling a 7 is a 1/6 chance.  The chance of rolling a 2 is a 1/18 chance. 
+
+>**Question 2:** Comment on the variation of values among the simulation runs.  Is 100 rolls sufficient to determine the relative frequency of all the possible rolls?
+
+**Answer 2:** Everytime we ran our simulation the numbers changed because it was at random.  Since it was random I didn't see any consistency.  Therefore, I don't believe 100 rolls is sufficient to determine the relative frequency of all the rolls.
+
+>**Quesiton 3:** How did increasing the number of simulations affect the results?
+
+**Answer 3:** Increasing the number of simulations gives us more sufficient results.  The results were much close to being consistent for example, for 2 the range was anywhere from .24 to .34 in the ratio which is pretty close. 
+
+>**Question 4:**  How many rolls per simulation does it take before you can accuarately predict the probability of rolling 7 to 3 significant digits five times in a row? How about for the probability of rolling a 2?
+
+**Answer 4:** The amount of rolls per simulation it takes to accurately predict the probablility of rolling a 7 is about 1000 rolls to get if five times in a row.  To roll a 2, its about 5000 rolls to get it five times in a row.

src/Histogram.java

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+public class Histogram {
+  private int[] hist = new int [13];
+  private int totalRolls = 0;
+
+  public void tally(int roll) {
+   hist[roll] += 1;
+   totalRolls += 1;
+  }
+
+  public int getCount(int roll) {
+
+    return hist[roll];
+  }
+
+  public double getRatio(int roll) {
+
+    return hist[roll] / (double)totalRolls;
+  }
+
+  public void print() {
+    for (int  i= 2; i <= 12; i++) {
+      System.out.println(i + ": " + getCount(i) + " " + getRatio(i));
+  }
+}
+}

src/SimulationRunner.java

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+public class SimulationRunner {
+  public static void main(String[] args) {
+  Die d1 = new Die();
+  Die d2 = new Die();
+
+  Histogram hist = new Histogram(); 
+
+  for (int count = 0; count < 5000; count++) {
+    d1.roll();
+    d2.roll();
+
+    hist.tally(d1.getUpValue() + d2.getUpValue());
+  }
+
+  hist.print();
+  }
+}