<story><title>Paradoxes of probability and other statistical strangeness</title><url>https://theconversation.com/paradoxes-of-probability-and-other-statistical-strangeness-74440</url></story><parent_chain><item><author>p1esk</author><text>It did not get any more intuitive for me.</text></item><item><author>casta</author><text>If you see this problem as a special case of another problem the answer becomes pretty intuitive.&lt;p&gt;Suppose there are N (let&amp;#x27;s pick 1000) doors:
Behind one door is a car; behind the others N-1 (999), goats.
You pick a door, say No. 1, and the host, who knows what&amp;#x27;s behind the doors, opens N-2 (998) doors, excluding No. 1, which have have goats.&lt;p&gt;Now there are only two doors closed, the one you picked No. 1, and one that was part of N-1 (999) doors.
He then says to you, &amp;quot;Do you want to pick door No. 1 or the other one?&amp;quot;
Is it to your advantage to switch your choice?</text></item><item><author>pmoriarty</author><text>My favorite probability paradox has always been the Monty Hall problem[1]:&lt;p&gt;&lt;i&gt;Suppose you&amp;#x27;re on a game show, and you&amp;#x27;re given the choice of three doors:&lt;/i&gt;&lt;p&gt;&lt;i&gt;Behind one door is a car; behind the others, goats.&lt;/i&gt;&lt;p&gt;&lt;i&gt;You pick a door, say No. 1, and the host, who knows what&amp;#x27;s behind the doors, opens another door, say No. 3, which has a goat.&lt;/i&gt;&lt;p&gt;&lt;i&gt;He then says to you, &amp;quot;Do you want to pick door No. 2?&amp;quot;&lt;/i&gt;&lt;p&gt;&lt;i&gt;Is it to your advantage to switch your choice?&lt;/i&gt;&lt;p&gt;[1] - &lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;en.wikipedia.org&amp;#x2F;wiki&amp;#x2F;Monty_Hall_problem&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;en.wikipedia.org&amp;#x2F;wiki&amp;#x2F;Monty_Hall_problem&lt;/a&gt;</text></item></parent_chain><comment><author>yellowstuff</author><text>Let me try. Say you pick the prize door initially. Obviously, if you switch you will now have a non-prize door.&lt;p&gt;Say you pick one of the two non-prize doors initially. The host now opens the other non-prize door, leaving only the prize door. If you switch you get the prize door.&lt;p&gt;So switching always changes the prize door to a non-prize door and a non-prize door to the prize door. You start on the prize door 1&amp;#x2F;3 of the time and a non-prize door 2&amp;#x2F;3, so you should always switch.</text></comment>
<story><title>Paradoxes of probability and other statistical strangeness</title><url>https://theconversation.com/paradoxes-of-probability-and-other-statistical-strangeness-74440</url></story><parent_chain><item><author>p1esk</author><text>It did not get any more intuitive for me.</text></item><item><author>casta</author><text>If you see this problem as a special case of another problem the answer becomes pretty intuitive.&lt;p&gt;Suppose there are N (let&amp;#x27;s pick 1000) doors:
Behind one door is a car; behind the others N-1 (999), goats.
You pick a door, say No. 1, and the host, who knows what&amp;#x27;s behind the doors, opens N-2 (998) doors, excluding No. 1, which have have goats.&lt;p&gt;Now there are only two doors closed, the one you picked No. 1, and one that was part of N-1 (999) doors.
He then says to you, &amp;quot;Do you want to pick door No. 1 or the other one?&amp;quot;
Is it to your advantage to switch your choice?</text></item><item><author>pmoriarty</author><text>My favorite probability paradox has always been the Monty Hall problem[1]:&lt;p&gt;&lt;i&gt;Suppose you&amp;#x27;re on a game show, and you&amp;#x27;re given the choice of three doors:&lt;/i&gt;&lt;p&gt;&lt;i&gt;Behind one door is a car; behind the others, goats.&lt;/i&gt;&lt;p&gt;&lt;i&gt;You pick a door, say No. 1, and the host, who knows what&amp;#x27;s behind the doors, opens another door, say No. 3, which has a goat.&lt;/i&gt;&lt;p&gt;&lt;i&gt;He then says to you, &amp;quot;Do you want to pick door No. 2?&amp;quot;&lt;/i&gt;&lt;p&gt;&lt;i&gt;Is it to your advantage to switch your choice?&lt;/i&gt;&lt;p&gt;[1] - &lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;en.wikipedia.org&amp;#x2F;wiki&amp;#x2F;Monty_Hall_problem&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;en.wikipedia.org&amp;#x2F;wiki&amp;#x2F;Monty_Hall_problem&lt;/a&gt;</text></item></parent_chain><comment><author>Jedd</author><text>The most succinct description I&amp;#x27;ve ever found of why you switch was so good I made a note of it, though sadly not the provenance:&lt;p&gt;&amp;quot;If you stay with the door you picked initially you succeed if the initial door has a car, which has a chance of 1&amp;#x2F;3. If your strategy is to switch then you succeed if your initial pick is a goat, which has a chance of 2&amp;#x2F;3.&amp;quot;</text></comment>