MathDB

Ahuiliztli is playing around with some coins (pennies, nickels, dimes, and quarters). She keeps grabbing

k

coins and calculating the value of her handful. After a while, she begins to notice that if

k

is even, she more often gets even sums, and if

k

is odd, she more often gets odd sums. Help her prove this true! Given

k

coins chosen uniformly and at random, prove that. the probability that the parity of

k

is the same as the parity of the

k

coins' value is greater than the probability that the parities are different.

Problem Statement