bag of marbles

Atwood's machine ] [ bag of marbles ] balance moon stone ] ball up/down ] bead parabola accelerometer ] boat anchor lake ] boat time ] bobbin on incline ] bosun's chair ] bouncing ball ] bowling ball rolling ] bug on band ] bursting shell ] falling chain ] Feynman's restaurant problem ] five pills ] flying cable ] forced pendulum ] gold mountain ] half pills ] hallway pole ] impelled rod ] inelastic relativistic collision ] infinite pulleys ] mass on an incline ] maximum angle of deflection ] packs of shirts ] particle in bowl ] particle in cone ] particle on sphere ] particle points parabola ] pile of bricks ] pion muon neutrino ] piston ramp spring ] plank weight trough ] rocket vs. jet ] roll without slipping ] rough inclined plane ] shooting marbles ] speedometer test ] three balls ] three logs ] turntable cart ] two rolling balls ] wheel and block ] whirling pendulum ] worlds fair ornament ]

service

This problem was suggested by statistician Brad Efron.

You have 100 marbles numbered 0 to 99 in a bag. You repeatedly draw a marble from the bag (all marbles being equiprobable), note its number, and replace it in the bag. On average, how many of the marbles numbered 1 through 99 will have been drawn from the bag one or more times before drawing marble #0?

Answer :


Solutions (listed by author)

Michael A. Gottlieb - the easy way (html, 2k)

Michael A. Gottlieb - a harder way (html, 3k)

 

Copyright 2000-2013 Michael A. Gottlieb. All rights reserved.