We are throwing darts on a disk shaped board of radius 5. We assumethat the position of the dart is a uniformly chosen point in the disk. The board hasa disk shaped bullseye with radius 1. Suppose that we throw a dart 2000 times atthe board. Estimate the probability that we hit the bullseye at least 100 times.

This is an example of a Binomial distribution, in which the chance of striking the dart here on the disc is:

Since this is a huge figure, one can use the central limit theory to approximate a supplied binomial distribution to a normally distributed one. As just a result, you have:

Since this is    a huge figure, one can use the central limit theory to approximate a supplied binomial distribution to a normally distributed one. As just a result, you have:

We must now calculate the likelihood of hitting the bullseye at least 100 times:

When we convert this to a conventional normal variable, we get:

When we use the conventional normal table to calculate this probability, we get:

Therefore the required probability is "0.0112".

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5% is the smallest probability

Step-by-step explanation:

5% = 0.05

2000 x 0.05 = 100 so the smallest chance is 5% but it could be more if you hit more bullseye