Monty Hall, the host of the TV game show "Let’s Make A Deal", shows you three curtains. One curtain conceals a valuable prize, while the other two conceal junk. All three curtains are equally likely to conceal the prize. He offers you the following "deal": pick a curtain, and you can have whatever is behind it. When you pick a curtain, instead of giving you what lies behind the curtain, Monty (who knows where the prize is) opens one of the remaining curtains to show you that there is junk behind it, and offers the following "new, improved deal": you can either stick with your original choice, or switch to the remaining (unopened) curtain. Amidst the deafening roars of "Stand pat!" and "Switch!" from the crowd, Monty points out that "previously your chances of winning were 1/3, and now, since you know that the prize is behind one of the two unopened curtains, your chances have increased to 1/2, and thus the new improved deal is indeed better."

Explanation:

I consider the Monty Hall game show problem to be a statistical illusion. This statistical illusion happens because your brain’s process of evaluating probabilities in the Monty Hall game show problem is usually on a false assumption. Statistical illusion is similar to optical illusions, the illusion seems more real than the actual answer.

To thoroughly view this statistical illusion, one needs to carefully break down the Monty Hall game show problem and identify the wrong assumptions. This process highlights how important it is to check that you’re clicking with the assumptions of a statistical analysis before trusting any of the results.

Monty Hall asks you to choose one of three doors in the show. One of the doors shields a prize and the other two doors contains no prize. You then loudly state out which door you pick, but you don’t get to open it right away. Monty then, opens one of the other two doors, and there, sit no prize behind it. At this stage, there are two closed doors containing one of which you picked. The prize sits behind one of the closed doors, but you can't tell which one.

Monty then asks you the ultimate question, “Do you want to switch doors?”. Majority of people assume that both doors are equally likely to have the prize. It seems like the door you chose has a 50/50 chance. Typically, there is no actual reason to change and most stick with their initial choice.  Theories were then speculated that switching doors doubles one's chances of winning the prize if they switch doors. Before, it was mere speculated theory but now, people are starting to see the sense behind it. Through a probability test, it is claimed that one has 66% chances of winning the prize if they switch doors over a 33% chance if they don't switch doors.

a. both connotative and denotative.

i have learned a great many things from participating in varsity football. it has changed my entire outlook on and attitude toward life. before my freshman year at [high-school], i was shy, had low self-esteem and turned away from seemingly impossible challenges. football has altered all of these qualities. on the first day of freshman practice, the team warmed up with a game of touch football. the players were split up and the game began. however, during the game, i noticed that i didn't run as hard as i could, nor did i try to evade my defender and get open. the fact of the matter is that i really did not want to be thrown the ball. i didn't want to be the one at fault if i dropped the ball and the play didn't succeed. i did not want the responsibility of the team because i was too afraid of making a mistake. that aspect of my character led the first years of my high school life. i refrained from asking questions in class, afraid they might be considered too stupid or dumb by my classmates. all the while, i went to practice and everyday, i went home physically and mentally exhausted.

yet my apprehension prevailed as i continued to fear getting put in the game in case another player was injured. i was still afraid of making mistakes and getting blamed by screaming coaches and angry teammates. sometimes these fears came true. during my sophomore season, my position at backup guard led me to play in the varsity games on many occasions. on such occasions, i often made mistakes. most of the time the mistakes were not significant; they rarely changed the outcome of a play. yet i received a thorough verbal lashing at practice for the mistakes i had made. these occurrences only compounded my fears of playing. however, i did not always make mistakes. sometimes i made great plays, for which i was congratulated. now, as i dawn on my senior year of football and am faced with two starting positions, i feel like a changed person.

over the years, playing football has taught me what it takes to succeed. from months of tough practices, i have gained a hard work ethic. from my coaches and fellow teammates, i have learned to work well with others in a group, as it is necessary to cooperate with teammates on the playing field. but most important, i have also gained self-confidence. if i fail, it doesn't matter if they mock or ridicule me; i'll just try again and do it better. i realize that it is necessary to risk failure in order to gain success. the coaches have always said before games that nothing is impossible; i know that now. now, i welcome the challenge. whether i succeed or fail is irrelevant; it is only important that i have tried and tested myself.

the topic of this essay is how the applicant has matured and changed since his freshman year. he focuses on football. one of the strengths of this essay is that it is well organized. the applicant clearly put time into the structure and planning of this essay. he uses the platform of football to discuss and demonstrate his personal growth and development through the high school years. what he could have done better was spend more time describing himself after he made improvements. as it is, he only tells us about his newfound confidence and drive. this essay would have been stronger had he actually shown us, perhaps by including a story or describing an event where his confidence made a difference

explanation: