A rain of meteors is falling on a circular area, with a radius of 10 km, so that each meteor is falling in a random place inside the area, without any dependancy on other meteor falls. assuming that the number of meteors that fall inside the round area is a poisson random variable with the parameter 2, and that the three assumptions of the poisson prccess are valid in the area where the meteors fall:
1)inside the 10km circle, we mark(create) another 6 km circle. if we know that inside of the bigger circle(the 10 km one), 4 meteors exactly had fallen, what is the probability that exactly one of them fell inside the 6k inner circle?
2)assuming that the meteorite rain repeats itself 5 times, exactly as written, so there's no dependancy between its repititions, what are the odds that exactly 2 times (from the 5), at least 3 meteorites will fall inside the bigger circle?
how do you answer such a question? i'm lost, so i really don't know what to write or how to explain. using the formula of the poisson $\sum_{n=0}^\infty \frac{\gamma ^n e^{- \gamma}}{n!}$
i think that for the second question, we are looking for the case where p(x=3), which would've been easier, but i don't know how to check for at least 2 out of 5 times here, is it just a regular 2 out of 5 binom case?
just to clarify, the small circle(6km radius) is inside the bigger circle(10km radius)