Probability/statistics question

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Homework Statement


During World War II, a hypothetical city laid out as a 10-by-10 grid of equal size blocks was hit by 200 randomly dropped bombs. Thus, the probability of any particular bomb hitting a specific city block was 1/100 and each block was hit by an average of 2 bombs. Find the probability of a given city block not being hit at all.



Homework Equations





The Attempt at a Solution



1 - (1/100) = P(not being hit).

Just wondering if this was correct and if the fact that an average of 2 bombs and 200 bombs droped would have an impact on the probablity of not being hit.
 
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Each block is hit on average TWO times so it seems reasonable to me that the probability you calculated should represent the probability that the bomb was a failure on BOTH "tries".
 
No, the question is asking for the chance that after 200 bombs were dropped, a particular block had not been hit.

You are right that P(not getting hit by a single bomb) = 99/100. So what's P(not getting hit by any of 200 bombs)?
 
is the answer P(not getting hit) = 0.00495
 
No. How did you get that?
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...

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