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 ?