44727题。让我们做个交易:犯罪心理

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玩家有三扇门可以选择:一扇门后面是一辆车;在其他人后面的是山羊。玩家选择一扇门，比如1号门，然后主人会立即打开这扇门，或者打开另一扇门，比如3号门，里面可能有汽车或山羊。如果主人打开了3号门，门后面有一只山羊，他就会让玩家选择，“你想选择2号门吗?”<ol><li>主机可以打开任何门，包括玩家选择的门。主持人可以打开一扇门，里面要么是山羊，要么是汽车。</li><li>主机并不总是提供在原来选择的门和关闭的门之间切换的机会。</li></ol>为了操纵游戏玩法，主机并不总是(一致地)随机地将汽车隐藏在门后。相反，根据之前的游戏统计，主机决定Pc的概率。<pre> Pc = [pc_1 pc_2 pc_3] pc_i是主机将车放在门i后面的概率。</pre>如果玩家最初选择了门D，那么主机对打开哪扇门的选择用一个条件概率矩阵Ph<pre> Ph = [ph_11 ph_12 ph_13 ph_21 ph_22 ph_23 ph_31 ph_32 ph_33]</pre>在上面的矩阵中，ph_ij表示如果汽车在门i后面，主机打开门j的概率。根据假设来解释矩阵意味着条件概率矩阵的所有元素ph_ij可以非零，约束条件是<pre> ph_i1 + ph_i2 + ph_i3 = 1，即主机必须总是打开门才能看到汽车或山羊。 </pre>On the game show, the host places the car behind a door with probability Pc in order to manipulate the outcome. The player then choose door D and the host, Monty Hall, opens door H using the conditional probability Ph.If the door H opened by the host has a goat behind it, what is the probability Pws that the player will win the car by switching the initial door choice to the door remaining?If switching option is not available (i.e. host always opens a door with the car behind it) return NaN.

“让我们做个交易”的游戏如下:玩家有三扇门可供选择:一扇门后面是一辆车;在其他人后面的是山羊。玩家选择一扇门，比如1号门，然后主人会立即打开这扇门，或者打开另一扇门，比如3号门，里面可能有汽车或山羊。如果主人打开了3号门，门后面有一只山羊，他就会让玩家选择，“你想选择2号门吗?”游戏玩法遵循以下规则:#主人可以打开任何门，包括玩家选择的门。主人可以打开一扇门，里面要么是山羊，要么是汽车。#主人并不总是提供在原来选择的门和关闭的门之间切换的机会。为了操纵游戏玩法，主人并不总是(一致地)随机地将汽车藏在门后。相反，根据之前的游戏统计，主机决定Pc的概率。 Pc = [pc_1 pc_2 pc_3] pc_i is the probability of the host placing car behind door i. If the player initially picks door D, then the host's choice of which door to open is represented by a conditional probability matrix Ph Ph = [ ph_11 ph_12 ph_13 ph_21 ph_22 ph_23 ph_31 ph_32 ph_33 ] In the above matrix, ph_ij represents the probability that the host opens door j given that the car is behind door i. Interpreting the matrix in terms of the assumptions implies that all elements ph_ij of the conditional probability matrix can be nonzero with the constraint that ph_i1 + ph_i2 + ph_i3 = 1 i.e. the host must always open a door to reveal the car or a goat. On the game show, the host places the car behind a door with probability Pc in order to manipulate the outcome. The player then choose door D and the host, Monty Hall, opens door H using the conditional probability Ph. If the door H opened by the host has a goat behind it, what is the probability *Pws* that the player will win the car by switching the initial door choice to the door remaining? *If switching option is not available (i.e. host always opens a door with the car behind it) return NaN.*

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最后的解决方案2019年2月7日提交

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斯蒂芬格塞尔2018年9月5日

看起来2B部分中的测试用例是不正确的。

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