airplane-seat-assignment-probability.html

<p><code>n</code> passengers board an airplane with exactly <code>n</code> seats. The first passenger has lost the ticket and picks a seat randomly. But after that, the rest of the passengers will:</p>

<ul>
	<li>Take their own seat if it is still available, and</li>
	<li>Pick other seats randomly when they find their seat occupied</li>
</ul>

<p>Return <em>the probability that the </em><code>n<sup>th</sup></code><em> person gets his own seat</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 1.00000
<strong>Explanation: </strong>The first person can only get the first seat.</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 2
<strong>Output:</strong> 0.50000
<strong>Explanation: </strong>The second person has a probability of 0.5 to get the second seat (when first person gets the first seat).
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
</ul>