MathDB

9

Part of 2015 AMC 12/AHSME

Problems(2)

Probability Cheryl Draws Double

Source: 2015 AMC 12A #9

2/4/2015
A box contains 22 red marbles, 22 green marbles, and 22 yellow marbles. Carol takes 22 marbles from the box at random; then Claudia takes 22 of the remaining marbles at random; and then Cheryl takes the last two marbles. What is the probability that Cheryl gets 22 marbles of the same color?
<spanclass=′latex−bold′>(A)</span>110<spanclass=′latex−bold′>(B)</span>16<spanclass=′latex−bold′>(C)</span>15<spanclass=′latex−bold′>(D)</span>13<spanclass=′latex−bold′>(E)</span>12<span class='latex-bold'>(A) </span>\dfrac1{10}\qquad<span class='latex-bold'>(B) </span>\dfrac16\qquad<span class='latex-bold'>(C) </span>\dfrac15\qquad<span class='latex-bold'>(D) </span>\dfrac13\qquad<span class='latex-bold'>(E) </span>\dfrac12
probabilitySupportAMC 10AMC
Balls and Bottles

Source: 2015 AMC12B #9

2/26/2015
Larry and Julius are playing a game, taking turns throwing a ball at a bottle sitting on a ledge. Larry throws first. The winner is the first person to knock the bottle off the ledge. At each turn the probability that a player knocks the bottle off the ledge is 12\frac{1}{2}, independently of what has happened before. What is the probability that Larry wins the game?
<spanclass=′latex−bold′>(A)</span>12<spanclass=′latex−bold′>(B)</span>35<spanclass=′latex−bold′>(C)</span>23<spanclass=′latex−bold′>(D)</span>34<spanclass=′latex−bold′>(E)</span>45<span class='latex-bold'>(A) </span>\frac{1}{2}\qquad<span class='latex-bold'>(B) </span>\frac{3}{5}\qquad<span class='latex-bold'>(C) </span>\frac{2}{3}\qquad<span class='latex-bold'>(D) </span>\frac{3}{4}\qquad<span class='latex-bold'>(E) </span>\frac{4}{5}
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