In Problem 10, find the probability that Team B scores the first goal. That is, find the probability that at least one goal is scored in the game and the first goal is scored by Team B.

Problem 10

Two teams A and B play a soccer match. The number of goals scored by Team A is modeled by a Poisson process N₁(t) with rate λ₁ = 0.02 goals per minute, and the number of goals scored by Team B is modeled by a Poisson process N₂(t) with rate λ₂ = 0.03 goals per minute. The two processes are assumed to be independent. Let N(t) be the total number of goals in the game up to and including time t. The game lasts for 90 minutes.