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The bomber blew up the car at about 8:00 am (0500 GMT) at the main entrance of the Hout prison in Taji, about 25 kilometres (15 miles) north of Baghdad, officials from the interior and defence ministries said.
The interior ministry official said 11 people were killed and 20 wounded, while the defence ministry official put the toll at 11 dead and 15 wounded.
Both spoke on condition of anonymity.