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Probability in Game Shows

Math behind Game Shows : Probability .
by

JC Romero

on 26 February 2013

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Transcript of Probability in Game Shows

Timeline 2013 2009 2010 2011 2012 Spill it to Win it! 0 + - = 9 8 7 1 2 3 4 5 6 c Introduction Probability problems are often among the hardest math concepts for students to wrap their heads around.
A game show is a type of entertainment genre in which contestants, television personalities or celebrities, sometimes as part of a team, play a game which involves answering questions or solving puzzles usually for money and/or prizes. Let's Make a Deal! Many game shows were made famous because of the excitement that the game brought to the audience. These game shows utilized probability puzzles to their advantage. Mechanics Spill It to Win It! is a game show based from Monty Hall’s paradox and from the famous Filipino game show, “Pera o Bayong”. A contestant is to be chosen randomly from the crowd. Where's the twist? The twist here is that when the content of the boxes will be revealed, the contestant must be ready for its contents: egg white, sand, mud, soil, or the grand prize itself. That is, if the contestant continues to play after the host offers another amount higher than the previous. Either way, the box will be opened to show the audience no disparity. Conclusion The Monty Hall paradox paved way for the success of game shows in our present generation. The theories and concepts of probability were realized through real life applications. At the same time, it gave a new perspective on game shows: winning isn’t just about the luck, it’s more on weighing the odds. Using probability concepts, a contestant can actually increase his/her chance of winning the game. The Monty Hall paradox also proved that switching yields a higher probability of winning than sticking to your original choice. It is a simple application of probability concepts that can easily be replicated and can actually turn an ordinary probability concept into a lively and exciting game show. Objective The group is tasked... Math in Game Shows The Probability One famous probability puzzle is The Monty Hall problem that is loosely based on the American television game show, Let's Make a Deal. Monty Hall Paradox It was named after the show's original host, Monty Hall. The problem, also called the Monty Hall paradox, is a veridical paradox because the result appears impossible but is demonstrably true. The Monty Hall paradox describes and gives explanation to the following situation. A game show contestant is invited to choose one of three doors, behind one of which is a good prize (a car) and two of which contains a bad prize. The contestant is then shown what's behind one of the two remaining doors and is offered a chance to change his/her selection. Through experimental and theoretical probability, it can be shown that the contestant gains a distinct advantage by changing his/her selection - something that foxed many Mathematicians. create a game show that would demonstrate probability. The game that would be created should increase the network’s rating. More than creating a game show, the group is challenged to make the game interesting and inviting to the audience. With these objectives, the group came up with a game, Spill It to Win It! He is to select a box from a group of five. The host will now open two boxes that do not have the grand prize (1,000,000 cash) and would later offer the contestant a certain amount. If the contestant continues to play, the host will then open another box and again, an amount will be offered. When there will only be two boxes remaining, the host will offer the contestant the chance to switch his box. 1.When you choose Box 1, your odds of winning are clearly 1/5. The probability concept can be simplified in the following statements: 2.The odds that the prize is behind Box 2, Box 3, Box 4, or Box 5 is 4/5. 3.When the host reveals that the grand prize is not inside Box 5, Box 4, Box 3, it doesn’t change the original probabilities. There is still a 4/5 chance that the prize is inside Box 2, Box 3, Box 4, or Box 5 . (Knowing the contents of the Box 2 doesn’t change the odds once you’ve started playing.) Therefore, Box 2 now has a probability of 4/5 that it contains the grand prize of 1,000,000 pesos. Given the following probabilities, it is more practical to switch than to stick to your first box. Clearly, 1/5 or 20% is way much smaller than 4/5 or 80% probability. In the end, the decision is for the contestant to make. 'The Economist' In this analysis the words, 'say No. 1', and 'say No. 3' in the question are not taken to mean that we are only to consider the case where the player has chosen door 1 and the host has revealed a goat behind door 3. The problem is solved by considering the equally likely events that the player has initially chosen the car, goat A, or goat B (Economist 1999):
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