This webpage is trying to type the word "evolution" by randomly selecting each character from the alphabet. The chance that each letter will be selected correctly is 1/26. The chance that every letter would be selected correctly is (1/26)9 (raised to the ninth power), or 1 out of 5,429,503,678,976. The chance of winning the lottery is 1 out of 13,983,816 (based on six different numbers randomly drawn from a set of balls numbered 1 through 49).
The word "evolution" is only 9 characters. However, to get a correct strand of DNA for the simple virus fX174, 390 characters are needed (from which it can choose from either A-C-T-G [Adenine-Cytosine-Thymine-Guanine]). So the probability of getting the correct order of gene sequencing is one out of 4390. This is essentially 6.4x10238. However, probabilities less than 1 in 1050 are considered statistically impossible.
While this analysis seems crude and oversimplified, a number of researchers have spent more than 10 years developing the most biologically realistic computer simulation program in the world to study genetic mutation over time. The program is called Mendel's Accountant. This program has been used to argue against the theory of evolution and is discussed in John Sanford's book Genetic Entropy: the Mystery of the Genome (4th edition). One paper that addresses this same problem with the biological and statistical rigor it deserves is the following:
Sanford, J., Brewer, W., Smith, F., & Baumgardner, J. (2015). The waiting time problem in a model hominin population. Theoretical Biology and Medical Modelling, 12(1), 18.
This waiting time problem was recently discussed in the following YouTube video: Mathematical Challenges to Darwin's Theory of Evolution.
