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| − | ==Problem==
| + | #redirect [[2014 AMC 12B Problems/Problem 22]] |
| − | In a small pond there are eleven lily pads in a row labeled <math>0</math> through <math>10</math>. A frog is sitting on pad <math>1</math>. When the frog is on pad <math>N</math>, <math>0<N<10</math>, it will jump to pad <math>N-1</math> with probability <math>\frac{N}{10}</math> and to pad <math>N+1</math> with probability <math>1-\frac{N}{10}</math>. Each jump is independent of the previous jumps. If the frog reaches pad <math>0</math> it will be eaten by a patiently waiting snake. If the frog reaches pad <math>10</math> it will exit the pond, never to return. what is the probability that the frog will escape being eaten by the snake?
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| − | <math> \textbf {(A) } \frac{32}{79} \qquad \textbf {(B) } \frac{161}{384} \qquad \textbf {(C) } \frac{63}{146} \qquad \textbf {(D) } \frac{7}{16} \qquad \textbf {(E) } \frac{1}{2} </math>
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| − | ==Solution==
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| − | Using the techniques of a Markov chain, we can eventually arrive to the answer of, is <math>\boxed{{(C)}\frac{63}{146}}</math>
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| − | ==See Also==
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| − | {{AMC10 box|year=2014|ab=B|num-b=24|after=Last Problem}}
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| − | {{MAA Notice}}
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