For this assignment, you will design, implement, and experiment with a class that models a weighted coin.

Part 1: Implementing the class

The constructor for your WeightedCoin class should have an integer parameter specifying the likelihood of obtaining HEADS from a random flip. For example, suppose you entered 50 at the BlueJ prompt when creating a WeightedCoin object. That coin would then have a 50% chance of producing HEADS on any given flip. If you specified 90, however, then each flip would have a 90% chance of being HEADS.

Your class should have the following methods.

String flip()

Returns either "HEADS" or "TAILS", with the likelihood of obtaining "HEADS" determined by the input to the constructor. For example, a WeightedCoin object constructed with input 75 should have a 75% chance of returning "HEADS".

int getNumberOfFlips

Returns the number of times the coin has been flipped so far.

double getPercentageOfHeads

Returns the percentage of "HEADS" (0.0 - 100.0) obtained so far, or 0.0 if no flips.

You should consider having a a Die object as a field of your class, as a 100-sided die would be extremely useful in determining the outcome of a flip. Since there is no reason to have more than one 100-sided die, you can make this field static so that it is shared by all WeightedCoin objects.

As before, your code should demonstrate good style. The class should have a comment block that describes its purpose, as well as your name (under @author) and date (under @version). Similarly, each method should have comment block that describe its behavior as well as any parameters (under @param) and return values (under @return). Statements should be consistently indented to highlight structure, and all method/variable names should be meaningful.

Part 2: Adding repetition

Testing your class to ensure that it behaves correctly can be a tedious task. For example, suppose you created a WeightedCoin object with a 60% likelihood of producing HEADS on a given flip. If you flipped that coin 10 times, you wouldn't necessarily obtain 6 out of 10 HEADS. Instead, you might get 5, or 7, or even something farther off. When the number of flips is small, a few extra lucky HEADS (or unlucky TAILS) can greatly skew the statistics. It is only when the number of repetitions is large that these lucky/unlucky stretches balance out and you get consistent results. More formally, the Law of Large Numbers states that the percentage of HEADS will approach the expected value as the number of repetitions approaches infinity.

Add the following method to your WeightedCoin class:

Use this method to verify the behavior described by the Law of Large Numbers. In particular, create three different coins, each with a different likelihood of obtaining HEADS (50%, 75%, and 90%). Then, make calls to the repeatedFlips method and report the percentage of HEADS for each coin after 10, 100, 1,000, and 10,000 flips. Do the percentages appear to be converging on the expected values?