# Probability word problem

1. May 2, 2005

Hello, I have been stuck on this problem for about a week and a half. I was wondering if there was anyone out there who might understand it and explain it clearly to me.

Suppose a volume of 1000 drops of water contains 2000 bacteria, separate from each other and thoroughly mixed in the water. A single drop is smeared uniformly over the surface of the dish. The dish contains nutrients on which the bacteria feed and multiply. After a few days, wherever a bacterium was deposited on the dish a visible colony of bacteria appears. Find the distribution of the number of colonies that appear. (a) over the whole plate, and (b) over an area of half the plate.

2. May 2, 2005

### BicycleTree

You should use the Poisson distribution. You know what the mean should be?

Or to be exact, you could use the binomial distribution where each success is finding a particular bacterium of the 2000 in the drop, so n = 2000 and you can figure out p. But the Poisson should be very accurate.

3. May 3, 2005