The Pill Problem, Lattice Paths and Catalan Numbers
نویسندگان
چکیده
A certain pill bottle contains m large pills and n small pills initially, where each large pill is equivalent to two small ones. Each day the patient chooses a pill at random, if a small pill is selected, (s)he eats it; otherwise (s)he breaks the selected pill and eats one half, replacing the other half, which thenceforth is considered to be a small pill. (a) What is the expected number of small pills remaining when the last large pill is selected? (b) On which day can we expect the last large pill to be selected?
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Counting Lattice Paths by Gessel Pairs
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