SOLUTION: 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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Question 1179544: 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.

Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!

Answer by ikleyn(52858)   (Show Source): You can put this solution on YOUR website!
.
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.
~~~~~~~~~~~~~~~~~~~~~


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    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  =  = .    ANSWER




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 = ,   


giving the same answer.

Solved.

---------------

If you want to learn about this subject and this class of problems,  look into the lesson
    - Rolling a pair of fair dice
in this site.  You will find there many similar solved problems.


Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic  "Solved problems on Probability".


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.



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