Context : The Tarantula Nebula in the Large Magellanic Cloud is our closest view of a starburst region and is the ideal environment to investigate important questions regarding the formation , evolution and final fate of the most massive stars .

Aims : We analyze the multiplicity properties of the massive O-type star population observed through multi-epoch spectroscopy in the framework of the VLT-FLAMES Tarantula Survey .
With 360 O-type stars , this is the largest homogeneous sample of massive stars analyzed to date .

Methods : We use multi-epoch spectroscopy and variability analysis to identify spectroscopic binaries .
We also use a Monte-Carlo method to correct for observational biases .
By modeling simultaneously the observed binary fraction , the distributions of the amplitudes of the radial velocity variations and the distribution of the time scales of these variations , we derive the intrinsic current binary fraction and period and mass-ratio distributions .

Results : We observe a spectroscopic binary fraction of 0.35 \pm 0.03 , which corresponds to the fraction of objects displaying statistically significant radial velocity variations with an amplitude of at least 20 km s ^ { -1 } .
We compute the intrinsic binary fraction to be 0.51 \pm 0.04 .
We adopt power-laws to describe the intrinsic period and mass-ratio distributions : f ( \log _ { 10 } P / \mathrm { d } ) \sim ( \log _ { 10 } P / \mathrm { d } ) ^ { \pi } ( with \log _ { 10 } P / \mathrm { d } in the range 0.15-3.5 ) and f ( q ) \sim q ^ { \kappa } with 0.1 \leq q = M _ { 2 } / M _ { 1 } \leq 1.0 .
The power-law indexes that best reproduce the observed quantities are \pi = -0.45 \pm 0.30 and \kappa = -1.0 \pm 0.4 .
The period distribution that we obtain thus favours shorter period systems compared to an Öpik law ( \pi = 0 ) .
The mass ratio distribution is slightly skewed towards low mass ratio systems but remains incompatible with a random sampling of a classical mass function ( \kappa = -2.35 ) .
The binary fraction seems mostly uniform across the field of view and independent of the spectral types and luminosity classes .
The binary fraction in the outer region of the field of view ( r > 7.8 \arcmin , i.e . \approx 117 pc ) and among the O9.7 I/II objects are however significantly lower than expected from statistical fluctuations .
The observed and intrinsic binary fractions are also lower for the faintest objects in our sample ( K _ { \mathrm { s } } > 15.5 mag ) , which results from observational effects and the fact that our O star sample is not magnitude-limited but is defined by a spectral-type cutoff .
We also conclude that magnitude-limited investigations are biased towards larger binary fractions .

Conclusions : Using the multiplicity properties of the O stars in the Tarantula region and simple evolutionary considerations , we estimate that over 50 % of the current O star population will exchange mass with its companion within a binary system .
This shows that binary interaction is greatly affecting the evolution and fate of massive stars , and must be taken into account to correctly interpret unresolved populations of massive stars .