Probability dice rolling

[believeagain2014]

I'm stuck with this multiple choice question and would love some help.
A student rolls a number cube (sides labeled 1 through 6) twice. What is the probability that the first or second result is the number 5?
Answer key states the answer is 11/36

 

[mmm4444bot]

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[pka]

I'm stuck with this multiple choice question and would love some help.

A student rolls a number cube (sides labeled 1 through 6) twice. What is the probability that the first or second result is the number 5?
Answer key states the answer is 11/36

In standard mathematical parlance, a number cube (sides labeled 1 through 6) is call a die one member of a pair of dice.
The outcome space is the set of thirty-six ordered-pairs:
${(1,1)}~\&~{(1,2)}~\&~{(1,3)}~\&~{(1,4)}~\&~{(1,5)}~\&~{(1,6)}\\ {(2,1)}~\&~{(2,2)}~\&~{(2,3)}~\&~{(2,4)}~\&~{(2,5)}~\&~{(2,6)}\\ {(3,1)}~\&~{(3,2)}~\&~{(3,3)}~\&~{(3,4)}~\&~{(3,5)}~\&~{(3,6)}\\ {(4,1)}~\&~{(4,2)}~\&~{(4,3)}~\&~{(4,4)}~\&~{(4,5)}~\&~{(4,6)}\\ {(5,1)}~\&~{(5,2)}~\&~{(5,3)}~\&~{(5,4)}~\&~{(5,5)}~\&~{(5,6)}\\ {(6,1)}~\&~{(6,2)}~\&~{(6,3)}~\&~{(6,4)}~\&~{(6,5)}~\&~{(6,6)}$
Of those thirty-six pair, eleven pairs have at least one five.
So the probability is $\dfrac{11}{36}$