The Monty Hall Paradox Essay Example

A paradox is a tool that promotes critical thinking. It evokes thought out of the complex structure of the situations it presents. It makes sense and does not make sense at the same time. The Oxford Dictionary defines a paradox as a statement that contains well-founded thinking from valid premises but at the same time presents a contradiction or a conclusion that is logically unacceptable. The report presents situations that are interrelated and can exist simultaneously but contradict simultaneously. The presence of opposite facts renders the statements difficult to understand and provide a complexity that elicits deep thought and often are the genesis of arguments between individuals who perceive them differently (Colie, 2015). The result is discussions that increase the ability to critically think within individuals. The factors named above provide the paradox with an essential role in the growth of a human being.

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The common understanding of a paradox is fundamental. It is considered a statement that reflects truth and false simultaneously. The expression of difference in opinion is another angle to view the subject of a paradox. The creation of a paradox is based on specific themes. Themes familiar to most people include contradiction, infinite regress, self-reference and mixing up of various levels of abstraction - the use of language and manipulation of contexts births exciting paradoxes. Thought-experiments have also been utilized to develop paradoxes that offer intriguing points of discussion. The different approaches applied in the creation of a paradox must achieve the basis of a paradox which is to produce a contradiction that stimulates the thinking of any individual trying to make sense of the statements. The achievement of this yearns the statement the right of consideration as a paradox.

Paradoxes have been classified using the Quine's classification to distinguish the different types. The first class is the veridical paradox. The paradox, in this case, produces a statement that is strange and after consideration is considered false. The falsidical paradox is described as one that provides an explanation that appears false and after consideration is false. The example for this kind of paradox is the "Achilles and the Tortoise paradox" that suggests in a race where the tortoise is given a head start, Achilles would not catch up to the tortoise since the tortoise would cover a certain fraction of distance every time Achilles reaches the tortoise's original point. In real life, the paradox did not make sense as the head start could be outdone by a faster runner. Mathematically, this could not be proven at the genesis of the paradox, but with the invention of convergent series, this could be explained and hence the falsidical paradox.

The final classification is a paradox that is neither of the two mentioned and is named antimony. The paradox, in this case, is defined by its proper application as it produces a better method of reasoning that is acceptable. It is considered a crisis in thought. The example commonly used to explain this is the "grandfather paradox" where the grandson goes back in time to kill the grandfather but the issue is, if the grandfather is executed, the father won't be born, and hence the son will be nonexistent. This offers a twist that is logical but at the same time provides a crisis in reasoning. The antimony's can be real and at the same time cannot be false.

The Monty Hall paradox was presented on an American Television game show named "Let's Make a Deal." The name of the paradox was derived from the host of the show, Monty Hall. The problem was a brain teaser the game used on the participants. The prize was a car that the participant would get if they landed a correct choice. The basis of the game was partly probability. The competition involved three doors for instance door 1, door 2 and door 3. All the doors either contained a goat or a car upon opening by the participant. The participant picks one door, and the show host with the knowledge of what is behind each door opens another door either 2 or 3 that contains a goat. The assumptions made in this game is that the host will always a door that includes a goat and that after every game the starting point is with three doors available (James, Friedman, Louie, & O'Meara, 2018).

The host then offers you the opportunity to change the door pick out of the two left that have not been opened. The problem is with deciding if it provides you an advantage by improving your pick or maintaining your original choice. The host has provided information by opening one door and eliminating it by revealing that behind it was a goat which is not the participant's prize leaving two doors for consideration. The participant has already picked the first door and must now decide whether to change if they think it will increase chances or retain and maintain the initial opportunities.

The critical question to the participant is whether to change or maintain the door, and this has been the basis of discussions and arguments among people trying to provide a solution to this problem. The question for this essay is to determine whether the Monty Hall paradox is a paradox. An article by (Hartley, 2018) states that most people understand the problem wrongly including the highly educated with Ph.D. in statistics and probability.

The reasoning of some is that the action of opening one door and revealing what it contains leaves the participant with a fifty-fifty chance of getting the prize. The group with this opinion are either right or wrong, and the contradiction arises.

The participant first had a probability of 1:3 when the first pick was made as all doors were closed and they did not know the contents of the all the three doors. The probability of this situation is that in the presence of three contestants, two will make the wrong choice and pick the door without the prize. However, the opening of one door and the lack of the award improves the odds to 1:2 as the doors up for opening are only two. There exist a 1:2 chance that his first choice was wrong and hence the reasoning that he should change to the second door. The participant could win the grand-prize by maintaining the original decision, but the knowledge of this is only available at the end of the game show. The odds have improved, and hence a section will support the maintenance. One door is eliminated so automatically the participant is more likely to win.

The second school of thought refutes the fifty-fifty chance once one door has been eliminated. The rationale is that by maintaining the first choice the odds do not change and despite the elimination of one door, the participant still has a 1:3 chance of selecting the correct door. This is because the first choice was made before the door was opened and therefore the chances are maintained with the maintenance of the original decision.

The option to change provides the participant with the opportunity to play game anew altogether. The new game starts with a 1:2 chance of winning since from the outset only two doors are open unlike the 1:3 prospect from the three doors initially.

According to this reasoning, the issue of changing doors serves as a distraction from the actual opportunity which is one to play a new game with better chances than the first one. This two opinions on the need to change provide a contradiction similar to the one a paradox provides.

The paradox suggests that the change of the pick is the right move. Mathematically, this theory is supported as the change improves the odds of winning. The game played repetitively with the option of changing every time results in a win for the change two out of 3 times compared to the possibility of maintaining which leads to one out three times win. The option of not changing is viewed psychologically as the frequent difficulty of the human mind to accept change once a decision is made and therefore the resistance against change and the justification of the fifty-fifty chance of picking the right door.

Marilyn Vos Savant wrote a column in a magazine in 1990 advising the contestants against retaining their original pick. The article suggested that the contestant should always change once the first door is opened and two options are left. The reasoning behind it was the first choice had the odds of getting a goat in two doors. Once one door was opened, the possibility of getting a goat reduced as there was only one goat left, but this advantage would extend to the contestant who made a change. The contestant who stuck to the first pick did not improve their chances as their pick made the opening of one door insignificant and they held to the possibilities similar to those at the start of the game.

The assumptions made include the information possessed by the contestant when the second decision is requested from them. The contestant now knows one door that has a goat contrary to the beginning when all doors had the same possibility of a goat or the grand prize. The maintenance of the first choice adds no value to the door chosen while the action of the host to reveal one door with a goat adds value to the door left hence the sense in changing to this door.

The switching of doors after the host reveals one door is not a random action of picking a door similar to the first round. The second step is an informed decision that evaluates the probability as more information has been acquired that guides the actions are taken. The different behaviors of the contestant explain their choice and affect the outcome of the game.

The response to the article was significant most of which was resistance to her theory. Notably, about one thousand of the respondents were Ph.D. holders with vast knowledge on different matters and whose opinion was highly regarded by society. The theory by Savant was vindicated by probability studies and from simulations of the challenge that confirmed the change improved the chances of acquiring the grand prize.

The Monty Hall paradox is a veridical paradox. A veridical paradox is one that produces a strange statement that is contradictory and complex to understand but upon consideration is found to be true. The paradox of the doors is a complex one that pits one school of thought against another. The fifty-fifty assumption is supported by a particular group as their opinion but when the alternate view is considered, mathematically the problem is explained and despite the one out of three chance that the fifty-fifty group partially proves their point, the reasoning behind changing every time is adequately supported.

This, therefore, provides a paradox to an individual who has not understood the explanation. The new player will most probably pick the first choice of not changing as it resonates with fundamental human thinking and may resist the introduction of the new idea. The information provided after that will enable the participant to change tact and increase their chances.

The paradox in this is that two situations or options are provided, and both seem to contradict each other. The first look at both options will give a complexity in the understanding of the two theories and create a conflict in the mind of the participant. The lack of information will lead the player into confusion not knowing which method is right or wrong because each technique has the possibility of landing them the grand prize. However, the introduction of new information on the chances of winning provided by the two options will convince the participant to adopt the more likely approach which is changing after the revelation of the door by the show host as the odds have changed and so should the choice.

Conclusion

The Monty Hall ca...