What Is the Probability of the Man Catching the Bus?

Alexsandro
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Interesting question about probability. Someone could help me to find the answer ?
"One bus arrives in the bus station between [12:58 am, 1:02 pm] and wait 15 seconds before to go out. One man arrives in the station bus between [12:59 am, 1:01 pm] and wait 30 seconds before to take a tax. What's the probability of the man to take the bus ? The time is continuous."
 
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I don't see anything interesting about it- it just doesn't make sense. The man arrives on the bus and waits 30 seconds before taking a taxi? Why should he get back on the bus?? Are we to assume that the bus would go in the same direction as he would take a taxi??
 
this is probably a homework problem relating to elementary statistics. Show us your suggestion on how you would adequately account for the problem. hint: find the ranges of the time intervals and the overlap.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

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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