Wednesday, June 3, 2020

06/03/2020 (2019: AMC 8, Problem 18)

Q: The faces of each of two fair dice are numbered 1, 2 , 3, 5, 7, and 8. When the two dice are tossed, what is the probability that their sum will be an even number?

$\textbf{(A) }\frac{4}{9}\qquad\textbf{(B) }\frac{1}{2}\qquad\textbf{(C) }\frac{5}{9}\qquad\textbf{(D) }\frac{3}{5}\qquad\textbf{(E) }\frac{2}{3}$

We create a table and put the outcomes of one roll on both sides:

We then write the sum of the column and the row of each (so if the column says 3 and the row is 8, then the sum in 8 + 3 = 11): 

We will highlight the even numbers:

There are 20 even outcomes out of the 36 total possible outcomes, making the answer 20/ 36 = 5/9, which is C.


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