Help with probability/statistics question.?

Posted on 2015-11-24 06:34:00 in Statistics by ANTHONY

The bombing of London during World War II was studied by statisticians as a Poisson random variable. One of the goals was to determine whether the Germans were bombing randomly or could target speci?c areas. London was divided into a grid consisting of 576 squares, each of area 0.25 square kilometers, and the number of bombs that landed in each grid square was counted. The total number of bombs that fell was 538. The statisticians found that the number of grid squares on which exactly two bombs fell was 93. What is the expected number of grid squares on which exactly two bombs landed if the bombs were dropped at random over the grid?

The answer I got for this was ~99 squares.

For the next question: what is the expected number of grid squares on which more than two bombs landed?
I got ~39 squares.

So far, it's been simple enough substitution into the poisson distribution formula, but these next two questions are giving me bother and I have no idea where to start..?

1.) Suppose that bombs were dropped on Liverpool during the war at a rate of 2 per square kilometer. A grid square in Liverpool and another in London are sampled at random. What is the probability that no bombs landed on either of these grid squares?

2.) Consider the two grid squares in the previous question. Given that a total of four bombs landed in the two grid squares, what is the probability that exactly three landed in the London grid square?

I don't know how to apply the poisson formula here..?

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