There is 3% coral coverage in a sea area of l=200m b=5m. The size(diameter) of each coral is 50 cm. If we throw a block of 1m2 in the area. How many coral will get hit by the block?(probability

I dont even know where to start.

Even a small hint will be really appreciated.

Thanks!

I don't have the knowledge required to solve this problem, but I had some fun trying

to establish a footing. To rough out a start, it was simpler to use squares rather than

circles for both coral and block shapes. From the data, it's straightforward to find

the number of corals (120). I wanted to see what the situation looked like for a

uniform distribution of corals, and I chose a grid of equilateral triangles spread over

the sea area. Thus all 120 corals were equidistant (4.3 meters) from each other.

From the geometry, it's clear that the probability of a "hit" on a coral is not high.

I was able to deduce a probability of about 0.18

With random distributions (placements) of corals, clustering also means more

empty space, so it's not clear whether or not probabilities of hits will increase

or decrease compared to the uniform case . In the extreme case of clustering

where all 120 corals are bunched together, there is then mostly empty sea and

a very low probability of hits. I suspect that the uniform distribution case is the

case of maximum probability of hits. If so, I think that's the end of it. The

answer to the question then is that probabilities vary from a high of about

0.18 downward.

Art