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:

n=52n=10m=4

First, think of what you know. you know that the number t the end of the equation will need to be subtracted because it is the money he lost from buying the lawn mower. and your first two weeks have negative profit, so that tells you that c and d are wrong. now you can plug any of the weeks into a and b to see which one works. i'll start with plugging week 1 into a.this isn't right because it says your answer for week one should be -90.so now we need to try the same thing with b.this one got you the right answer, (sometimes if you only check with one of the weeks multiple will work so you need to check with more of the weeks, but it worked out fine here)this means that b is the correct answer.let me know if you need more clarification. i hope this : )

4if you add the absolute values together