The intrinsic fraction of broad absorption line quasars (BALQSOs) is important in constraining geometric and evolutionary models of quasars. We present the fraction of BALQSOs in 2MASS detected quasars within the SDSS DR3 sample in the redshift range of 1.7 < z < 4.38. The fraction of BALQSOs is 40.4^{+3.4}_{-3.3}% in the 2MASS 99% database K_s band completeness sample, and 38.5^{+1.7}_{-1.7}% in the larger 2MASS sample extending below the completeness limit. These fractions are significantly higher than the 26% reported in the optical bands for the same parent sample. We also present the fraction of BALQSOs as functions of apparent magnitudes, absolute magnitudes, and redshift in the 2MASS and SDSS bands. The 2MASS fractions are consistently higher than the SDSS fractions in every comparison, and the BALQSO fractions steadily increase with wavelength from the SDSS u to the 2MASS K_s bands. Furthermore, the i - K_s color distributions of BALQSOs and non-BALQSOs indicate that BALQSOs are redder than non-BALQSOs, with a K-S test probability of 2e-12. These results are consistent with the spectral difference between BALQSOs and non-BALQSOs including both the absorption troughs and dust extinction in BALQSOs, which leads to significant selection biases against BALQSOs in the optical bands. Using a simple simulation incorporating the luminosity function of quasars and the amount of obscuration for BALQSOs, we simultaneously fit the BALQSO fractions in the SDSS and 2MASS bands. We obtain a true BALQSO fraction of 43\pm2% for luminous quasars (M_{K_s} \lesssim -30.1 mag).

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