Six balls are at the front of the classroom, and six students are each assigned a different colored ball.
Then they are asked to go up one at a time and take the ball they were assigned.
However, the first student doesn't like the color he was assigned, so he picks randomly from the remaining five.
After that, each successive student takes the color they were assigned if it's available, otherwise they choose randomly from the remaining balls.
What is the probability that the last student gets the ball they were assigned?
(In reply to related problem
by Steven Lord)
Given that in the case where the first student has equal likelihood of taking any student's color including his own, we can use a pair of conditional probabilities to compute the current situation where it's known he does not choose his own: let the latter probability be x and consider there are n students all together:
1/n + ((n-1)/n) * x = 1/2
x = (1/2 - 1/n) * n/(n-1) = (n/2 - 1)/(n - 1)
Substituting n = 6 as in the current instance, the answer to the current puzzle is indeed x = (3 - 1) / 5 = 2/5.
Posted by Charlie
on 2019-04-25 14:26:53