airplane-seat-assignment-probability

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Algorithms

<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:

<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>

Return the probability that the <code>nth</code> person gets his own seat.

&nbsp;
Example 1:

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

Example 2:

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

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= n &lt;= 105</code></li>
</ul>

nthPersonGetsNthSeat

Airplane Seat Assignment Probability

Brainteaser

Math

Dynamic Programming

Probability and Statistics

有 <code>n</code> 位乘客即将登机，飞机正好有 <code>n</code> 个座位。第一位乘客的票丢了，他随便选了一个座位坐下。

剩下的乘客将会：

<ul>
	<li>
	如果他们自己的座位还空着，就坐到自己的座位上，
	</li>
	<li>当他们自己的座位被占用时，随机选择其他座位</li>
</ul>

第 <code>n</code>&nbsp;位乘客坐在自己的座位上的概率是多少？

&nbsp;

示例 1：

<pre>
输入：n = 1
输出：1.00000
解释：第一个人只会坐在自己的位置上。</pre>

示例 2：

<pre>
输入: n = 2
输出: 0.50000
解释：在第一个人选好座位坐下后，第二个人坐在自己的座位上的概率是 0.5。
</pre>

&nbsp;

提示：

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