How do you arrive at this answer? There are four nucleotides, A, T, G, C that ma

Question

How do you arrive at this answer?

There are four nucleotides, A, T, G, C that make up DNA.

A genome has a GC content of 40% within intergenic regions, and 50% within gene regions. The proportion of the genome lying inside gene regions is 20%; the rest is intergenic. (Meaning P(G) = 0.2 and P(C) = 0.2; P(A) and P(T) both equal 0.4 for intergenic regions, and all 4 P(N) = 0.25 in gene regions)
A position in the genome is randomly sampled; the nucleotide at that position is a G. What, to three significant figures, is the posterior probability that the sampled position was in a gene region?

ANSWER: 0.238

Explanation / Answer

P(intergenic) = 0.8

P(within gene) = 0.2

P(N within gene) = 0.25 for N = A, G, C, T

P(A intergenic) = P(T intergnic) = 0.4

P(G intergenic) = P(C intergenic) = 0.2

P(within gene | G)

= P(within gene and G) /( P(within gene and G) + P(intergenic and G) )

= 0.2 * 0.25 /( 0.2 * 0.25 + 0.8 * 0.2 )

= 25 / 105

= 0.238

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