Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-02-18T14:22:58Z No. of bitstreams: 1 marcelosoaressalomao.pdf: 5275463 bytes, checksum: bd084577d98f83eca225c7117c8ee332 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-02-26T13:31:33Z (GMT) No. of bitstreams: 1 marcelosoaressalomao.pdf: 5275463 bytes, checksum: bd084577d98f83eca225c7117c8ee332 (MD5) / Made available in DSpace on 2016-02-26T13:31:33Z (GMT). No. of bitstreams: 1 marcelosoaressalomao.pdf: 5275463 bytes, checksum: bd084577d98f83eca225c7117c8ee332 (MD5) Previous issue date: 2014-08-16 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Nesse trabalho apresentamos o Paradoxo de Monty Hall e seus aspectos lúdicos como uma oportunidade de cativar o educando para o estudo das probabilidades. Oferecendo assim a oportunidade de trabalhar no universo da educação básica o ensino de probabilidade na sala de aula através de atividades em forma de jogos. Apesar da dificuldade do assunto na Educação Básica, os professores que lerem o trabalho poderão aproveitar algumas dessas ideias e transformá-las em conhecimento aos seus educandos. Primeiramente apresentamos um breve resumo teórico sobre probabilidade, um pouco da história do Monty Hall paradox e algumas soluções formais e experimentais. Para as atividades, há simulações do problema com variantes do números de portas proporcionando desenvolver no aluno as habilidades como: experimentação, abstração, modelagem. Com o intuito de fazer uso de recursos computacionais apresentamos uma sugestão de atividade com a utilização de um software de fácil acesso e manuseio. Isso se sustenta, pois com aumento de cursos tecnológicos e a presença maior da informática no cotidiano do educando é imperativo o emprego dessa interdisciplinaridade. / We present the Monty Hall Paradox and its entertaining aspects as a chance to engage the student to the study of probability. Thus offering the opportunity to work in the world of basic education by teaching probability in the level of classroom through activities in the form of games. Despite of the difficulty of the subject at the Basic Education, it is expected that teachers who read the work will take some of these ideas and turn them into knowledge to their students. First, we present a brief overview of theoretical probability, a little history of the Monty Hall paradox and some formal and experimental solutions. For activities, there are simulations of the problem with varying numbers of ports providing the development of student skills such as experimentation, abstraction, and modeling. In order to make use of computational resources we present a suggested activity with the use of software for easy access and handling. This is sustained, because with increased technological courses and the increased presence of computers in daily life of the student it is imperative the employment of this interdisciplinarity.

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In the Monty Hall Dilemma (MHD), three doors are presented with a prize behind one and participants are instructed to choose a door. One of the unchosen doors is then shown to not have the prize and the participant can choose to stay with their door or switch to the other one. The optimal strategy is to switch. Herbranson and Schroeder (2010) found that humans performed poorly on this task, whereas pigeons learned to switch readily. However, we found that pigeons learned to switch at level only slightly above humans. We also found that pigeons stay nearly exclusively when staying is the optimal strategy and when staying and switching are reinforced equally (Stagner, Rayburn-Reeves, & Zentall, 2013). In Experiment 1, rats were trained under these same conditions to observe if possible differences in foraging strategy would influence performance on this task. In Experiment 2, pigeons were trained in an analogous procedure to better compare the two species. We found that both species were sensitive to the overall probability of reinforcement, as both switched significantly more often than subjects in a group that were reinforced equally for staying and switching and a group that was reinforced more often for staying. Overall, the two species performed very similarly within the parameters of the current procedure.

In 1990’s, the circumstances of being a contestant on a popular game show were published in a trendy question and answer column in Parade Magazine. If contestant switched from the initial choice to a second choice offer by the host, would the chances of winning the desired prize be increase? The columnist’s response to the reader sparked a good deal of controversy among mathematicians. Shortly after the publication of this answer, articles appeared in various mathematical publications some supporting and some refuting the columnist’s answer. This document reports the results of research into the controversy generated by some of the probability problems used on Let’s Make a Deal game show. Using a variety of approaches and assumption, the author attempts to formulate mathematical proof to explain the correct answer to the contestant’s question, “Should I switch?” / text