Which of the following is primary allylic alcohol?

A primary allylic alcohol requires that the hydroxyl group is attached to a carbon adjacent to a carbon-carbon double bond (allylic) and that the hydroxyl-bearing carbon is only attached to one other carbon (primary).

Option A: $\mathrm{H_2 C=CH-CH(CH_3)-OH}$ is allylic and secondary.

Option C: $\mathrm{H_2 C=CH-C(CH_3)_2 -OH}$ is allylic and tertiary.

Option D: $\mathrm{CH_3 -CH=CH-CH(CH_3)-OH}$ is allylic and secondary.

Option B: $\mathrm{H_2 C=CH-CH_2 -OH}$ is allylic since the $\mathrm{CH_2}$ group is adjacent to the double bond, and primary as the hydroxyl-bearing carbon attaches to only one other carbon.

The correct primary allylic alcohol is $\boxed{B}$.