Application 2 - Probability Example of when gut feelings appear to have led to a failure My husband and I bought stock in a particular company, which we will call WXYZ. Our broker made a recommendation, and we had a strong gut feeling that purchasing 3,100 shares of WXYZ would be a good investment. Well, it looks like we were wrong. The company changed exchanges. The stock value has decreased significantly and has remained very low for months. It certainly appears that our gut reaction has failed us; however, we remain hopeful. Example of when gut feelings proved true My husband is a chronic kidney stone patient. As a result, he recognizes the painful symptoms. Recently, he felt he had a stone. In these situations, the sooner the stone is detected, an easier less complicated treatment can be applied. After spending the time, effort, and cost to see the urologist and go through the testing process, he was correct as a small stone was detected. He was able to drink plenty of fluids and get the stone out on his own. In this case, he did the right thing as if he had gambled and waited until the stone become larger, it would have required a more costly and more difficult treatment with more recovery time. In this case, acting on his gut feeling really paid off. MTH 157 - REAL STATISTICS APPLICATIONS Real Statistics Application for Content of Chapter 3 - Probability Classic Monty Hall: To Switch or Not to Switch, that is the question. Purpose This assignment will help you understand that probability is not always intuitive. Directions The problem: Suppose that you are a contestant on a game show and are confronted with three doors. There is a goat behind two of the doors and an automobile behind the remaining door. You select Door 1 and the host then says, \"at least one of the other doors has a goat behind it, so I am going to open such a door.\" The host opens Door 3 and then asks if you now want to switch from Door 1 to Door 2. In this activity, you want to determine if you should switch and if it matters whether you switch or not. Note: Suppose that the automobile is equally likely to be behind any of the three doors. When the car is behind Door 1, the host is equally likely to open Door 2 or Door 3. (This is the case for any of the doors.) The host always opens a bad door. The contestant is always given the option to switch. If the outcome of the first door is in first position, the outcome of door 2 in the second position, and the outcome of door 3 in the third position, then the sample space is the set S = {AGG, GAG, GGA}, where A stands for auto and G for goat. Solve the problem: Play the game. Visit the following website: http://www.grandillusions.com/simulator/montysim.htm a. Play the game a few times without switching doors. Stay with your first choice. Note the number of wins. b. Play the game the same number of times and switch doors each time after a door is opened. Note the number of wins. Clear all your results and run a simulation of the game. c. Simulate the game 1,000 times without switching doors. Choose keep the choice. Note the number of wins and calculate the probability of winning. d. Clear results and simulate the game 1,000 times switching doors. Choose change the choice. Note the number of wins and calculate the probability of winning. Present the problem and your solution to the others in the class: Should you switch when given the option to do so? Does it matter? What was your initial gut feeling when given the option to switch? Were the results surprising to you? Explain. Please share a couple of your own life experiences in which your gut feeling was correct and one in which it turned out to be incorrect. View the responses submitted by your classmates. Please respond to at least two other postings. Share similar experiences and whether you tend to give attention to your intuition and how your study of probability will affect your decision making