How does 2 independent variables combined correlate with a third variable?

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Let’s say that something is at least partially explained by the influence of 2 other different, independent things. For example If we say that the correlation bethween Body Hair score and CAG Repeats are 0.5, and that the correlation bethween Body Hair and Testosterone is 0.3, how would I then be able to calculate the correlation bethween both Testosterone and CAG Repeats combined with Body Hair score? Would I be able to calculate how well both Testosterone and CAG Repeats combined correlates with Body Hair score by multiplying the two independent correlations (for example: 0.5 + 0.3 = 0.8? Or would I need to use the coefficient of determination, or r squared, by doing this: 0.5 x 0.5=0.25 — 0.3 x 0.3=0.1 — 0.25+0.1 = 0.35? In order to determine to which degree those 2 independent variables together influences Body Hair?

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Knowing that two random variables, say $X,Y$, are independent of each other, and each has a known interdepence with a third random variable, $Z$, is not enough information to determine their joint conditional distribution when given $Z$.   You need to know how they are conditionally dependent given $Z$.

Similar to how knowing the marginal distributions is not alone sufficient to determine the joint distribution; knowledge of their dependence is required for that.