MathDB

The amount

2.5

is split into two nonnegative real numbers uniformly at random, for instance, into

2.143

and

.357

, or into

\sqrt{3}

and

2.5-\sqrt{3}.

Then each number is rounded to its nearest integer, for instance,

2

and

0

in the first case above,

2

and

1

in the second. What is the probability that the two integers sum to

3

<span class='latex-bold'>(A)</span>\ \frac{1}{4} \qquad<span class='latex-bold'>(B)</span>\ \frac{2}{5} \qquad<span class='latex-bold'>(C)</span>\ \frac{1}{2} \qquad<span class='latex-bold'>(D)</span>\ \frac{3}{5} \qquad<span class='latex-bold'>(E)</span>\ \frac{3}{4}

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