Question 1179544
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Find the conditional probability of the indicated event when two fair dice (one red and one green) are rolled.
The red one is 2, given that the sum is 7.
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<pre>
When two dice are rolling, the total space of events has 36 elements. 
These elements are the pairs (red,green),  where "red" and "green" are integer numbers from 1 to 6 inclusive.


These 36 elements of the space of events have equal probability of  {{{1/36}}}  each.


Of these 36 elements, exactly 6 (six) have the sum of 7:


    red     green

     1        6

     2        5

     3        4

     4        3

     5        2

     6        1


and only one pair  (red,green) = (2,5)  is favorable.


Therefore, the answer to the problem's question is 


    probability  P  = {{{((1/36))/((6/36))}}} = {{{1/6}}}.    <U>ANSWER</U>




I made this simple calculation using the full space of events.



But you can easily get the same answer using the REDUCED space of events.

It consists of 6 listed elements, and only one of them is favorable;  so


    P = {{{1/6}}},   


giving the same answer.
</pre>

Solved.


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If you want to learn about this subject and this class of problems, &nbsp;look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Rolling-a-pair-of-fair-dice.lesson>Rolling a pair of fair dice</A> 

in this site. &nbsp;You will find there many similar solved problems.



Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this online textbook under the topic &nbsp;"<U>Solved problems on Probability</U>". 



Save the link to this textbook together with its description


Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson


into your archive and use when it is needed.