MathDB

17

Part of 2002 AMC 10

Problems(3)

Sarah's weird coffee ritual

Source:

2/11/2008
Sarah pours four ounces of coffee into an eight-ounce cup and four ounces of cream into a second cup of the same size. She then transfers half the coffee from the first cup to the second and, after stirring thoroughly, transfers half the liquid in the second cup back to the first. What fraction of the liquid in the first cup is now cream? <spanclass=′latex−bold′>(A)</span> 1/4<spanclass=′latex−bold′>(B)</span> 1/3<spanclass=′latex−bold′>(C)</span> 3/8<spanclass=′latex−bold′>(D)</span> 2/5<spanclass=′latex−bold′>(E)</span> 1/2 <span class='latex-bold'>(A)</span>\ 1/4 \qquad <span class='latex-bold'>(B)</span>\ 1/3 \qquad <span class='latex-bold'>(C)</span>\ 3/8 \qquad <span class='latex-bold'>(D)</span>\ 2/5 \qquad <span class='latex-bold'>(E)</span>\ 1/2
Regular Octagon

Source:

2/27/2008
A regular octagon ABCDEFGH ABCDEFGH has sides of length two. Find the area of △ADG \triangle{ADG}. (A)\ 4 \plus{} 2 \sqrt{2} \qquad (B)\ 6 \plus{} \sqrt{2} \qquad (C)\ 4 \plus{} 3 \sqrt{2} \qquad (D)\ 3 \plus{} 4 \sqrt{2} \qquad (E)\ 8 \plus{} \sqrt{2}
geometrytrapezoid
Probability of Same vs. Different Color

Source:

4/2/2013
There are 10011001 red marbles and 10011001 black marbles in a box. Let PsP_s be the probability that two marbles drawn at random from the box are the same color, and let PdP_d be the probability that they are different colors. Find ∣Ps−Pd∣|P_s-P_d|.
<spanclass=′latex−bold′>(A)</span>0<spanclass=′latex−bold′>(B)</span>12002<spanclass=′latex−bold′>(C)</span>12001<spanclass=′latex−bold′>(D)</span>22001<spanclass=′latex−bold′>(E)</span>11000<span class='latex-bold'>(A) </span>0\qquad<span class='latex-bold'>(B) </span>\dfrac1{2002}\qquad<span class='latex-bold'>(C) </span>\dfrac1{2001}\qquad<span class='latex-bold'>(D) </span>\dfrac2{2001}\qquad<span class='latex-bold'>(E) </span>\dfrac1{1000}
probability