Settling a debaate

Question

There are three people sitting at a table. Person one decides to think of a number between 1-3. Person two will always get to choose first. Person three will choose second but has the chance of guessing the same number as the second person. Who has the best probability of winning and why?

Person one ( person who is picking the number

Person two (person who always goes first)

Person three (person who always chooses second)

Answer 1

Probability of guessing a correct

A=2^nd person wins- P(A)=1/3=0,33

B=3^rd person wins – P(B)=1/3=0,33

C=1^st person wins – P(C) = P(not A and not B)=P(notА)*P(notB)=(1-1/3)(1-1/3)=2/3*2/3=4/9=0,44.

Answer: Person one ( person who is picking the number).