Suppose there are 2 defectives among 5

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suppose there are 2 defectives among 5...

suppose there are 2 defectives among 5, test one at a time until you find the 2nd defective, find:

1.you need at most 3 tests
2.given the 2nd defective found at 3rd test, find the p that you find the 1st defective at 1st test.

Thanks.
 
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shinkansenfan said:
suppose there are 2 defectives among 5, test one at a time until you find the 2nd defective, find:

1.you need at most 3 tests
2.given the 2nd defective found at 3rd test, find the p that you find the 1st defective at 1st test.

Thanks.

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RGV
 
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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