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P15 [Combinatorics] - Turkish NMO 1st Round - 2002

Source:

August 8, 2014
probability

Problem Statement

There are 1010 seats in each of 1010 rows of a theatre and all the seats are numbered. What is the probablity that two friends buying tickets independently will occupy adjacent seats?
<spanclass=′latex−bold′>a)</span> 155<spanclass=′latex−bold′>b)</span> 150<spanclass=′latex−bold′>c)</span> 255<spanclass=′latex−bold′>d)</span> 125<spanclass=′latex−bold′>e)</span> None of above <span class='latex-bold'>a)</span>\ \dfrac{1}{55} \qquad<span class='latex-bold'>b)</span>\ \dfrac{1}{50} \qquad<span class='latex-bold'>c)</span>\ \dfrac{2}{55} \qquad<span class='latex-bold'>d)</span>\ \dfrac{1}{25} \qquad<span class='latex-bold'>e)</span>\ \text{None of above}
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