# Genetic Algorithm with Mutation

A genetic algorithm uses the following mutation operator: the bits in the input string are considered one by one independently, with probability 0.01 that each bit is inverted.

Given that you apply the mutation operator to the string (0 0 0 0), what is the probability that the output is:

(0 0 0 0)?

(0 1 0 0)?

(1 0 1 0)?

(1 1 1 1)?

Show the process of your computation.

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#### Solution Preview

As background, if events A and B are independent, then the chance the A and B both happen is P(A)*P(B).

In this problem, we are told that each input bit is considered independently, and has a 0.01 chance of being flipped. So for example, the chance that '0' would ...

#### Solution Summary

This solution shows how to calculate the probability of a certain output for a genetic algorithm with a mutation operator.