The following game was played on a popular television show. The host showed a contestant three large curtains. Behind one of the curtains was a nice prize (maybe a new car) and behind the other two curtains were worthless prizes (duds). The contestant was asked to choose one curtain. If the curtains are identified by their prizes, they could be labeled G, D1, and D2 (Good Prize, Dud1, and Dud2). Thus, the sample space for the contestants choice is S = {G, D1, D2}.1

If the contestant has no idea which curtains hide the various prizes and selects a curtain at random, assign reasonable probabilities to the simple events and calculate the probability that the contestant selects the curtain hiding the nice prize.

Before showing the contestant what was behind the curtain initially chosen, the game show host would open one of the curtains and show the contestant one of the duds (he could always do this because he knew the curtain was hiding the good prize). He then offered the contestant the option of changing from the curtain initially selected to the other remaining unopened curtain. Which strategy maximizes the contestants probability of winning the good prize: stay with the initial choice or switch to the other curtain? In answering the following sequence of questions, you will discover that, perhaps surprisingly, this question can be answered by considering only the sample space above and using the probabilities that you assigned to answer part (a).

If the contestant chooses to stay with her initial choice, she wins the good prize if and only if she initially chose curtain G. If she stays with her initial choice, what is the probability that she wins the good prize?

If the host shows her one of the duds and she switches to the other unopened curtain, what would be the result if she had initially selected G?

Answer the question in part (ii) if she had initially selected one of the duds.

If the contestant switches from her initial choice (as the result of being shown one of the duds), what is the probability that the contestant wins the good prize?

Which strategy maximizes the contestants probability of winning the good prize: stay with the initial choice or switch to the other curtain?

DO NOT WORRY ABOUT SOLVING THE PROBLEM JUST COMPLETE THE PROGRAMMING ASSIGNMENT IN JAVA.

- Programming - P34 Solve 2.20. Followed by writing a java program that plays this game. - Have it play this game 10,000 times and not change the door it picked - Have it play this game 10,000 times, and change the door it picks every time - No scanner, have the game handle everything - Remember \% is number of wins over total number of trials (10,000) Do not put more than 4 lines of code in your main method