Question 1137809
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The full space of events is the set of all pairs  (i,j), where i and j are integer numbers from 1 to 6, inclusively.

This space consists of  6*6 = 36 elements.


Of them, the outcomes where the sum is 8 or greater, are


    sum  8 :  (2,6), (3,5), (4,4), (5,3), (6,2)     In all, 5 pairs.

    sum  9 :  (3,6), (4,5), (5,4), (6,3)            In all, 4 pairs.

    sum 10 :  (4,6), (5,5), (6,4)                   In all, 3 pairs.

    sum 11 :  (5,6), (6,5)                          In all, 2 pairs.

    sum 12 :  (6,6)                                 Only    1 pair.


Thus the number of events where the sum is 8 or greater is  5 + 4 + 3 + 2 + 1 = 15.


Of them, the number of pairs, where at least one component is 4, is equal to 5 : (4,4), (4,5), (5,4), (4,6) and (6,4).


Starting from this point, you can find the answer to the problem's question in two ways.
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<U>1-st way.  &nbsp;&nbsp;"Naive"</U>


<pre>
The probability under the question is  {{{5/15}}} = {{{1/3}}}.    <U>ANSWER</U>
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<U>2-nd way - Formal</U>


<pre>
    The probability to have the sum >= 8  

        P1 = P( sum >= 8) = {{{15/36}}};


    The probability to have the sum >= 8 AND at least one component 4  

        P2 = P(sum >= 8 AND at least one component 4) = {{{5/36}}};


     Therefore, the conditional probability under the question is  P = {{{P2/P1}}} = {{{((5/36))/((15/36))}}} = {{{5/15}}} = {{{1/3}}}.    <U>ANSWER</U>
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Solved.