MathDB
Probability of Modified Fair Dice

Source:

January 18, 2009
probability

Problem Statement

Two six-sided dice are fair in the sense that each face is equally likely to turn up. However, one of the dice has the 4 4 replaced by 3 3 and the other die has the 3 3 replaced by 4 4. When these dice are rolled, what is the probability that the sum is an odd number? <spanclass=latexbold>(A)</span> 13<spanclass=latexbold>(B)</span> 49<spanclass=latexbold>(C)</span> 12<spanclass=latexbold>(D)</span> 59<spanclass=latexbold>(E)</span> 1118 <span class='latex-bold'>(A)</span>\ \frac{1}{3}\qquad <span class='latex-bold'>(B)</span>\ \frac{4}{9}\qquad <span class='latex-bold'>(C)</span>\ \frac{1}{2}\qquad <span class='latex-bold'>(D)</span>\ \frac{5}{9}\qquad <span class='latex-bold'>(E)</span>\ \frac{11}{18}