probability question 13

Question

the probability that a certain comet colliding with a planet is approximately 1.5 x 10^-7 every time their orbits intersect. What is the probability that during 600,000 orbit intersections, at least one collision occurs?

Answer 1

The main concept here is the "at least one" part.

 

In order to find the probability of "at least one" event, we can use the formula: P(at least one success) = 1 – P(no successes).

 

In the context of this problem, we should figure out the P(no successes) first, then tackle the "at least one" problem.  P(no success in 600,000 trials)=0.913931 (this was found using a Poisson distribution).  Therefore, P(at least one success) = 1 – 0.913931 = 0.086  So there is an 8.6% chance that at least one comet collision occurs in 600,000 orbit intersections.