On each round, ann and bob each simultaneously toss a fair coin. let xn be the number of heads tossed in the 2n flips which occur during the first n rounds. for each integer m > 0, let rm denote the probability that there exists an n such that xn = m.

Step-by-step explanation:

In a coin toss the  probability of tossing a head is 0.5 (50% head/50% tails)

If n is the number of rounds and 2n the number of coins tossed (one for each player), the probability of having m heads tossed is:

R is the number of cases (combination of coins tossed) that gives a m number of heads. Each case has a probability of so:

For example, to toss 4 heads in 5 rounds:

where is the picture

step-by-step explanation: