MathDB

Let

n

be a positive integer congruent to

1

modulo

4

. Xantippa has a bag of

n + 1

balls numbered from

0

n

. She draws a ball (randomly, equally distributed) from the bag and reads its number:

k

, say. She keeps the ball and then picks up another

k

balls from the bag (randomly, equally distributed, without repossession). Finally, she adds up the numbers of all the

k + 1

balls she picked up. What is the probability that the sum will be odd?

5