Probability (1 Viewer)

[seanieg89]

Chad O. Dude is on a date with a girl at an Italian restaurant. They are sharing a bowl of spaghetti
which contains exactly n pieces. They eat by simultaneously choosing an end of a piece of
spaghetti and sucking it into their mouths, then repeating this process.


Find the probability of Chad and his date finishing the bowl without trying to suck opposite ends of the
same strand of spaghetti.

 

[moll.]

Assuming they both eat strands at the same rate, then the prob that the person who chooses a strand to eat second (if they choose consecutively in approx n/2 rounds) will choose the same one as Chad (who is named after a country) is 1/n for the first go. If they do not coordinate, they try again, with prob 1/n-2 (because 2 different stands were eaten first round) and so on until end. Sum of results = prob of doing a Lady and the Tramp. Oddly enough, under my initial assumption, if there is an odd number of spaghetti strands then the prob is 100% as by the final strand you get prob 1/n-(n-1)=1.

Also, I have been drinking, so balls.

 

[moll.]

Also, as an addendum, I made mistakes last night. Missed the part that says they pick it up by the end. Which means there are 2n ends. If Chad (who is still named after a country) is already holding one of those ends then his date has the choice from 2n-1 ends in the first round, so has prob 1/[2n-1] of getting the end for the one Chad is holding. There are then 2(n-2)-1 ends in the second round and so on. Still the same problem for the last one if there is an odd number, in that the prob of picking up the same on is 1/{2(n-[n-1])-1}