SOLUTION: Suppose k identical boxes contained n balls numbered one through n. One ball is drawn from
each box. What is the probability that m is the largest number drawn?
Algebra.Com
Question 570976: Suppose k identical boxes contained n balls numbered one through n. One ball is drawn from
each box. What is the probability that m is the largest number drawn?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
For this problem we will assume that 
.
The best way is probably to try small cases (for m). Let P(m) be the probability that m is the largest number drawn. If m = 1, then every number drawn must be a 1, and
 = (\frac{1}{n})^k)
If m = 2, every number must be a 1 or a 2, and we would try to claim something like
 = (\frac{2}{n})^k)
However, this is incorrect, because this includes the case where every number is a 1 (which violates the constraint that at least one number must be a 2). To fix this, we subtract P(1):
 = (\frac{2}{n})^k - P(1) = (\frac{2}{n})^k - (\frac{1}{n})^k)
Finding P(3) is similar to finding P(2), except that we subtract P(2):
 = (\frac{3}{n})^k - P(2) = (\frac{3}{n})^k - (\frac{2}{n})^k +(\frac{1}{n})^k)
This generalizes to
 = (\frac{m}{n})^k - P(m-1))
, or
 = (\frac{m}{n})^k - (\frac{m-1}{n})^k + (\frac{m-2}{n})^k ... \pm (\frac{1}{n})^k)
where the plus/minus of (1/n)^k depends on the parity of m (i.e. if m is odd, +; if m is even, -).
RELATED QUESTIONS
Box M contains nine balls numbered 1 through 9 and box N contains five balls numbered 1... (answered by Edwin McCravy)
please help me solve this question;
A box contains 50 wooden balls numbered 1 through... (answered by math_helper)
A box contains N white and M black balls. Balls are randomly selected one at
a time,... (answered by ikleyn)
a box contains 6 identical red balls, 3 identical white balls and 5 identical black... (answered by Edwin McCravy)
Six billiard balls, numbered 1 through 6, are placed in a box. Three of the balls are... (answered by Fombitz)
A bag contains 9 red balls numbered 1,2,3,4,5,7,8,9 and 6 white balls numbered... (answered by stanbon)
A bag contains 9 red balls numbered 1,2,3,4,5,6,7,8,9 and 6 white balls numbered... (answered by Fombitz)
n a lottery game, a single ball is drawn at random from a container that contains 25... (answered by jim_thompson5910)
a box contains 25 balls numbered from 1 to 25.one ball is drawn at random.what is the... (answered by ramkikk66)