Our professor provides the answer to the question, but I\'m still having trouble

Question

Our professor provides the answer to the question, but I'm still having trouble getting there. The correct answer is 0.473. ONLY RESPOND IF YOU GET 0.473 AS THE ANSWER.

Here's the question.

You work in a planning office and municipal officials request your assistance with a question regarding firefighting services in one particular precinct. You conclude that fires occur randomly, with an average occurrence rate of 2.40 events/week. You are asked the following question: In a week that has at least one event, what is the probability that the number of events will be three or greater?

Again, the answer should be 0.473, but it's not clear how.

Explanation / Answer

= 2.4/week

P(X = x) = e- * x / x!

P(X > 1) = 1 - P(X = 0) = 1 - e-2.4 * 2.40 / 0! = 1 - 0.0907 = 0.9093

P( X > 3) = 1 - [P(X = 0) + P(X = 1) + P(X = 2)]

               = 1 - [e-2.4 * 2.40 / 0! + e-2.4 * 2.41 / 1! + e-2.4 * 2.42 / 2! ]

               = 1 - 0.5697

               = 0.4303

P(X > 3 | X > 1) = P(X > 3) / P(X > 1)

                          = 0.4303 / 0.9093

                          = 0.473 (ans)

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