First to Score Probablity

[wrongturn]

Let's say team A's probability to score on each possession is PA, and team B is PB. If team A gets ball first, is there a "simple" formula to calculate the probability for team A to score first? Like a formula to use in spreadsheet?

Yes, I want spoon feed, and flame if you want.

[Justin7]

In the two first possessions, the odds of each team scoring first are:
A: Pa
B: (1-Pa)(Pb)

If you assume someone scores, then the probability of A scoring first is Pa / [ Pa + (1-Pa)(Pb)]

You can get to that conclusion from using an infinite series, or limiting the probability space.

[wrongturn]

Justin7, thanks.