Sex-Linked Inheritance

Problem

The conditional probability of an event A given another event B, written Pr(A∣B), is equal to Pr(A and B) divided by Pr(B).

Note that if A and B are independent, then Pr(A and B) must be equal to Pr(A)×Pr(B), which results in Pr(A∣B)=Pr(A). This equation offers an intuitive view of independence: the probability of A, given the occurrence of event B, is simply the probability of A (which does not depend on B).

In the context of sex-linked traits, genetic equilibrium requires that the alleles for a gene k are uniformly distributed over the males and females of a population. In other words, the distribution of alleles is independent of sex.

Given: An array A of length n for which A[k] represents the proportion of males in a population exhibiting the k-th of n total recessive X-linked genes. Assume that the population is in genetic equilibrium for all n genes.

Return: An array B of length n in which B[k] equals the probability that a randomly selected female will be a carrier for the k-th gene.