Player A has n+1 coins, while B has n coins. Both players throw all of their coins simultaneously and observe the no. of heads. If all coins are fair, then what is the probability that A obtains more heads than B? A fair coin is independently flipped n times, k times by A and n − k times by B. Show that the probability that A and B flip the same number of heads is equal to the probability that there are a total of k heads?