MathDB

Kevin develops a method for shuffling a stack of

10

cards numbered

1

through

10

. He starts with the unshuffled pile, which is in perfect order with

1

at the top and

10

at the bottom. He takes the top card off the unshuffled pile and places it in what he calls the shuffled pile. Then, he flips a coin. If the coin is heads, he takes the card at the top of the unshuffled pile and places it at the top of the shuffled pile. If the coin comes up tails, he places the card at the at the bottom of the shuffled pile. He repeats this process for all the remaining cards. What is the probability that at the end of this shuffling, the top card is a prime number? Express your answer as a common fraction.

Problem Statement