Question 1132192
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 A pair of dice is rolled together till a sum of either 5 or 7 is obtained. Then probability that 5 comes before 7
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            As I read the problem,  I understand it in this way  (literally as it is written) :


<pre>
                A pair of dice is rolled together. As soon as a sum of either 5 or 7 is obtained, the experiment stops.

                What is the probability that the last obtained sum is 5 ?
</pre>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It is different from reading by @greenestamps, &nbsp;who counts when and how the &nbsp;"7" &nbsp;will be obtained after getting of &nbsp;"5".


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;In my interpretation, &nbsp;I do not concern what will happen after &nbsp;<U>EITHER</U> &nbsp;5 &nbsp;<U>OR</U> &nbsp;7 &nbsp;will be obtained - it is the command 
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;to stop the experiment.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Therefore, &nbsp;my solution is different, &nbsp;although the answer is the same number.



<U>Solution</U>


<pre>
P(5) = {{{4/36}}} = {{{1/9}}}       <<<---=== of  6x6 = 36 sample cases only 4 produce the sum of 5.


P(7) = {{{6/36}}} = {{{1/6}}}       <<<---=== of  6x6 = 36 sample cases only 6 produce the sum of 7.


The problem asks to find a conditional probability of getting the sum of 5 under the condition that this sum is <U>EITHER</U>  "5"  <U>OR</U>  "7".


Then this conditional probability is  {{{P(5)/P(5_or_7)}}} = {{{((4/36))/((4/36 + 6/36))}}} = {{{4/10}}} = {{{2/5}}} = 0.4 = 40%.       <U>ANSWER</U>
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