<PRE><B>Question 1201433</B>
&lt;font color=black size=3&gt;
Answers:
a) &lt;font color=red size=4&gt;1/3&lt;/font&gt;
b) &lt;font color=red size=4&gt;2/3&lt;/font&gt;


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Explanation:


I&#39;ll refer to the persons as C and D.
I&#39;ll also refer as the restaurants as R1,R2,R3.


Let&#39;s say C picks R1.
D has probability &lt;font color=red&gt;1/3&lt;/font&gt; of also picking R1.


This logic applies if C chose R2, or R3.
Effectively we can make person C the anchor, and have the question be reframed to &quot;What are the chances person D picked the anchor restaurant?&quot;. The order of the restaurants doesn&#39;t matter, and neither does the order of who selects first.


Therefore, the chances of them &lt;font color=red&gt;meeting&lt;/font&gt; is &lt;font color=red&gt;1/3&lt;/font&gt;


The chances of them &lt;font color=red&gt;missing&lt;/font&gt; each other is 1 - (1/3) = &lt;font color=red&gt;2/3&lt;/font&gt;


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Another approach:


Form a table showing all possible combos
C&#39;s choices are along the top
D&#39;s choices are along the left side
&lt;table border = &quot;1&quot; cellpadding = &quot;5&quot;&gt;&lt;tr&gt;&lt;td&gt;&lt;/td&gt;&lt;td&gt;R1&lt;/td&gt;&lt;td&gt;R2&lt;/td&gt;&lt;td&gt;R3&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;R1&lt;/td&gt;&lt;td&gt;X&lt;/td&gt;&lt;td&gt;&lt;/td&gt;&lt;td&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;R2&lt;/td&gt;&lt;td&gt;&lt;/td&gt;&lt;td&gt;X&lt;/td&gt;&lt;td&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;R3&lt;/td&gt;&lt;td&gt;&lt;/td&gt;&lt;td&gt;&lt;/td&gt;&lt;td&gt;X&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;
The X&#39;s refer to instances where they meet. Otherwise, they miss each other.


There are 3*3 = 9 outcomes total


There are 3 X&#39;s out of 9 slots total.
3/9 = &lt;font color=red&gt;1/3&lt;/font&gt; = chances of them &lt;font color=red&gt;meeting&lt;/font&gt;
6/9 = &lt;font color=red&gt;2/3&lt;/font&gt; = chances of them &lt;font color=red&gt;missing &lt;/font&gt; each other.


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Edit:


Another approach:


Using inspiration from the tutor @ikleyn, we can have the following
X = P(C picks R1, D picks R1) = P(C picks R1)*P(D picks R1) = (1/3)*(1/3) = 1/9
Y = P(C picks R2, D picks R2) = P(C picks R2)*P(D picks R2) = (1/3)*(1/3) = 1/9
Z = P(C picks R3, D picks R3) = P(C picks R3)*P(D picks R3) = (1/3)*(1/3) = 1/9


Then X+Y+Z = (1/9)+(1/9)+(1/9) = 3/9 = &lt;font color=red&gt;1/3&lt;/font&gt; represents the chances of them meeting, and &lt;font color=red&gt;2/3&lt;/font&gt; is the chance of them not meeting.
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