http://kenji.blog/en/tags/probability/Recent content in Probability on kenji.blogHugo -- gohugo.ioenkenjinoteSun, 31 Mar 2024 23:41:51 +0900http://kenji.blog/en/p/%E3%83%A2%E3%83%B3%E3%83%86%E3%82%A3%E3%83%9B%E3%83%BC%E3%83%AB%E5%95%8F%E9%A1%8C/Sun, 31 Mar 2024 23:41:51 +0900http://kenji.blog/en/p/%E3%83%A2%E3%83%B3%E3%83%86%E3%82%A3%E3%83%9B%E3%83%BC%E3%83%AB%E5%95%8F%E9%A1%8C/<img src="http://kenji.blog/p/%E3%83%A2%E3%83%B3%E3%83%86%E3%82%A3%E3%83%9B%E3%83%BC%E3%83%AB%E5%95%8F%E9%A1%8C/img_1.png" alt="Featured image of post Monty Hall problem" /><h2 id="what-is-the-monty-hall-problem">What is the Monty Hall problem? </h2><p>The Monty Hall problem is a brain teaser, in the form of a probability puzzle, loosely based on the American television game show &ldquo;Let&rsquo;s Make a Deal&rdquo; and named after its original host, Monty Hall. The problem is as follows:</p> <p>Premise: One of the three doors has a prize behind it, and the other two have a dud (goat).</p> <ol> <li>The participant chooses one of the three doors.</li> <li>The host opens one of the other two doors that the participant did not choose, revealing a dud.</li> <li>The participant is asked whether they want to change their chosen door.</li> </ol> <p>The problem is to consider whether the participant should change the door or not.</p> <h2 id="solution">Solution </h2><p>The solution to the Monty Hall problem is as follows:</p> <ol> <li> <p>If the participant does not change the initially chosen door</p> <ul> <li>Probability of winning: 1/3</li> <li>Probability of losing: 2/3</li> </ul> </li> <li> <p>After the host opens the dud door</p> <ul> <li>If not changed, probability of winning: 1/3 (Does not change from the winning probability in step 1.)</li> <li>If changed, probability of winning: 2/3 (The probability of the remaining options.)</li> </ul> </li> </ol> <p>Therefore, the participant has a higher probability of winning by changing the door.</p> <h2 id="reference">Reference </h2><ul> <li>Wikipedia <a class="link" href="https://en.wikipedia.org/wiki/Monty_Hall_problem" target="_blank" rel="noopener" >Monty Hall problem</a></li> </ul>