Question

At all times, a pipe-smoking mathematician carries 2 matchboxes—1 in his left-hand pocket and 1 in his right-hand pocket. Each time he needs a match, he is equally likely to take it from either pocket. Consider the moment when the mathematician first discovers that one of his matchboxes is empty. If it is assumed that both matchboxes initially contained N matches, what is the probability that there are exactly k matches, k = 0, 1, ... „N, in the other box?

Answer 1

The probability that there are exactly k matches in the other box, given that one box is empty, can be calculated using the binomial distribution.

Step-by-step explanation:

The probability that there are exactly k matches in the other box, given that one box is empty, can be calculated using the binomial distribution. Let's assume there are initially N matches in both boxes.

The probability of having k matches in the other box can be found using the formula for the binomial probability:

P(k matches) = C(N, k) * (1/2)k * (1/2)(N-k)

Where C(N, k) represents the number of ways to choose k matches from N matches, and (1/2)k represents the probability of getting k matches from the filled box and (1/2)(N-k) represents the probability of getting (N-k) matches from the empty box.