Bromine halohydrin question

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You will make two enantiomers with the same probability of formation; in other words you make a racemic mixture.
 
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Note that, you start with a cis compound which becomes a threo after anti addition; threo compounds cannot be meso!
Also, there is no plane of symmetry!
 
i dont understand why III is true, i thought you couldnt have a chiral center if there was a double bond.
 
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