Avoiding troublesome construction

A family of three was injured when their car collided with another car.

The above is a sentence quite commonly seen in newspapers.

'Family' can be regarded as singular when referred to as a group/unit. It can also be a plural noun when it is referring to members of the family.

The sentence in italics has a construction that treats 'family' as singular [as evidenced by the use of a singular (passive) verb 'was injured'] but as plural later with the use of a plural possessive adjective 'their'.

To avoid such irregularity, the sentence should have been A family of three were injured when their car collided with another car.