Solving Relativity Theory Probability Questions

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probability questions

I have some tasks and I don't know how should I solve them.

1) During transporting 3% percent of the goods get damaged. What is the possibility that among 6 chosen goods there will be
a) only one damaged
b) at least one damaged

2) The probability that a massage won't de delivered is 0,2. I have to find a probibility that among 400 masages
a) 90 will be delivered
b) no more then 50 won't be delivered

3) The probability of reaching the second level is 0,8 for the first person and 0,7 for the second. [ksi] is the number of people who reached the second level. I have to find the law of the distribution for [ksi].

P.S. sorry for my English
 
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Just out of curiosity, was there any reason for titling this "relativity theory"? Did you think more people would read than if you titled it "probability questions"?

In any case, you should have already read the regulations: show us that you have made some attempt on these problems yourself. They look to me like basic applications of the binomial probability formula.
 
Well, I,ve just solved the third one.
http://img46.imageshack.us/img46/2940/relat5ia.jpg

For the second I tried to use Poisson distribution but the numbers are too large to use it. Binomial probability doesn't help me too because the numbers are larger then 30.

In the first I don't even know how to start because we have percents there. I know a very good formulae but I can't use it here.
http://img46.imageshack.us/img46/247/relat13mw.jpg
 
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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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