perplexus.info :: Probability : Magic Bunny Power

Magic Bunny Power (Posted on 2024-08-04)

Your mother gifted you a chocolate bunny on your birthday. But this is a magic bunny. On the first night, the bunny either disappears or splits into two identical magic bunnies, with equal probability. The next night, if you have two bunnies, they each (independently) either disappear or split in two. And so it continues, each night any remaining bunnies each independently either disappear or split into two bunnies.

What is the probability that you will eventually be left with no magic bunnies?

No Solution Yet Submitted by Danish Ahmed Khan

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computer exploration

| Comment 1 of 7

ext=0; mx=0;

for trial=1:100000

bunnies=1;

for d=1:1000

newb=bunnies;

for i=1:bunnies

if rand<.5

newb=newb-1;

else

newb=newb+1;

end

bunnies=newb;

if newb==0

ext=ext+1;

% disp(d)

if d>mx

mx=d;

end

break

end

ext/trial

finds in over 99% of cases, all bunnies eventually die out. As the number of generation that are followed increases, the die-out gets closer and closer to complete, and the maximum day of die-out expands to near the limit of days followed.

Posted by Charlie on 2024-08-04 13:00:06

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