Possibility to create single donor-acceptor (D-A) pairs by attaching dye molecules to various sites of DNA strands with control of the inter-dye distance R enables one to measure average Förster resonance energy transfer (FRET) efficiency E as a function of R. Triplet states of the dyes influence the dependence E(R) considerably. Two types of FRET efficiency are considered: E = EA and E = ED. The efficiency EA(R) = JA(R)/[JA(R) + JD(R)] depends on the donor and the acceptor average intensities JD(R) and JA(R) measured in D- and A-fluorescence, whereas the efficiency ED(R) = 1 - JD(R)/JD(∞) depends only on the intensity of D-fluorescence, so-called the donor quenching method. The shape of the functions ED (R) and EA (R) depends strongly on whether the dyes have blinking fluorescence. FRET efficiencies ED (R) and EA (R) undergo the influence of many experimental factors and therefore, differ considerably from pure FRET efficiencies ED (s) (R) and EA (s) (R). Pure FRET efficiencies ED,A (s) (R) are calculated with the help of rate equations for D-A pairs, whose molecules have triplet states. It is shown how the calculated efficiencies ED,A (s) (R) can be compared to FRET efficiencies measured with the help of the intensities ID,A(R) corrected by cross talk and background light.