MathDB

12

Part of 2005 National Olympiad First Round

Problems(1)

P12 [Combinatorics] - Turkish NMO 1st Round - 2005

Source:

11/8/2013
Ali and Veli goes to hunting. The probability that each will successfully hit a duck is 1/21/2 on any given shot. During the hunt, Ali shoots 1212 times, and Veli shoots 1313 times. What is the probability that Veli hits more ducks than Ali?
<spanclass=′latex−bold′>(A)</span> 12<spanclass=′latex−bold′>(B)</span> 1325<spanclass=′latex−bold′>(C)</span> 1324<spanclass=′latex−bold′>(D)</span> 713<spanclass=′latex−bold′>(E)</span> 34 <span class='latex-bold'>(A)</span>\ \dfrac 12 \qquad<span class='latex-bold'>(B)</span>\ \dfrac{13}{25} \qquad<span class='latex-bold'>(C)</span>\ \dfrac{13}{24} \qquad<span class='latex-bold'>(D)</span>\ \dfrac{7}{13} \qquad<span class='latex-bold'>(E)</span>\ \dfrac{3}{4}
probability