Step 1: Prepare the master-mix by combining four equal volumes of dNTPs. For any one nucleotide in the master-mix: \[ C_{\text{each, master}} = 20~\text{mM}\times\frac{40}{40+40+40+40} = 20 \times \frac{40}{160} = 5~\text{mM}. \] Hence the total dNTP concentration in the master-mix is: \[ C_{\text{total, master}} = 4 \times 5~\text{mM} = 20~\text{mM}. \]
Step 2: Add \(4~\mu\text{L}\) of this master-mix to a final PCR volume of \(50~\mu\text{L}\). The dilution factor is: \[ \frac{4}{50} = 0.08. \] Therefore: \[ C_{\text{total, PCR}} = C_{\text{total, master}} \times 0.08 = 20~\text{mM} \times 0.08 = 1.6~\text{mM} = 1600~\mu\text{M}. \]
Step 3: Thus, the total dNTP concentration in the PCR mix is: \[ \boxed{1600~\mu\text{M}} \] which corresponds to: \[ 400~\mu\text{M} \ \text{each (dATP, dTTP, dGTP, dCTP)}. \]
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