So, what's the probability of winning if you always switch? 9/10Īnd, what's the probability of winning if you never switch? 1/10.Īn old puzzle and a good one. What's the probability of picking the wrong door the first time? 9/10 If you choose any of the 9 wrong doors the first time, switching will always make you win. If you choose the right door the first time, switching will make you lose. Monty will do a similar thing once you choose for the first time, but, instead of revealing 1 goat, he will reveal 8. What's the probability of choosing the wrong door the first time?Īnother expansion of the thought that several people have brought up: If you choose one of the two wrong doors the first time, switching will always make you win. If you choose the correct door the first time, switching will always make you lose. In the actual Monty Hall problem, you choose twice, and the probability of the second choice is affected by the first. In the case you've given, you are only choosing once. No, Syomantak, you're changing the situation in an essential way. But I love his explanation for the simplicity. It is more mathematically rigorous than Sal's demonstration, but I was a mathematics major at university. The notation really took work to put together. It only gives you information about * P(not A)*. Notice that Monte's new information tells you nothing about A. So, substituting, we end up withģ) Since P(B) = 0, Then we can substitute '0' for P(B), which gives us Using the last 2 certainties, we end up with the followingġ) P(not A) = P(B)+P(C). So, let's look at our certain probabilities:Į. So we have the following certain probability: Monte will never open the door with the prize, or he will be fired. This leads to the following probabilities:Ĭ Monte Opens 'B' - can be any door, but we can call any door he chooses 'B' You Choose 'A' - can be any door, but we can call any door you choose 'A' This is just a way of stating that the prize can be anywhere.ī. So I tried to break it down by probability of winning the car behind doors A, B or C.Ģ) P(A)+P(B)+P(C) = 1 (or 100%). That's why we're committed to bringing you the best game news and insights, so you can stay on top of the latest trends and developments in the gaming world.What makes the Monte Hal Problem interesting in that the host knows, and will always chose the goat. Our team is always on the ground, bringing you the latest news and updates straight from the source.Īt Game Bastion, we're passionate about gaming, and we know you are too. Stay ahead of the curve with our comprehensive coverage of gaming events, conferences, and expos. Our in-depth reviews and analysis will help you make informed decisions about your next gaming purchase, and our insider news and interviews with developers will give you a behind-the-scenes look at the gaming industry. Whether you're a hardcore gamer or a casual player, we have something for everyone. Our team of gaming experts is dedicated to providing you with the most accurate and up-to-date news on the latest releases and developments in the gaming world.įrom the latest consoles to PC gaming and mobile games, we cover it all. Are you looking for the latest updates in the world of gaming? Look no further than Game Bastion! We are your ultimate source for game news, reviews, and insights on the hottest titles in the industry.
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