Question

Thermodynamics and Statistical Mechanics problem

On episode 196 of MythBusters, Kari, Grant, and Tory test ”tastes like chicken”. There are 11 plates of fried chicken (C) and 9 plates of fried non-chicken (N) like snake, turtle, etc. numbered from 1 to 20 which are sampled one at a time by blindfolded tasters. An arrangement is an ordered set e.g. CCNNCNNNCNCC...; NCNCNCNCCCC...; etc.

A) What is the probability of randomly guessing the correct arrangement if the blind tasters know that there are 11 Cs and 9 Ns?

B) With the same knowledge, what is the probability of getting exactly one plate wrong?

C) What is the probability of randomly guessing the correct arrangement if the blind tasters do not know how many of the plates are chicken?

D) With the same knowledge, what is the probability of getting exactly one plate wrong?

Answer 1

A) The number of ways of distributing Cs and Ns is . The probability of guessing the correct arrangement is .

B) One plate out of 20 can go wrong. Therefore given there are 11 Cs and 9 Ns, 20 such sequences can go wrong. The required probability is

C) Since the taster does not know the number of plates that are chicken or non-chicken, There are a possible sequences of 20 characters.

The required probabilty is

D) As in part (B), The required probability is