How are these molecules chiral and achiral?

[![enter image description here](https://i.stack.imgur.com/JUGv4.png)](https://i.stack.imgur.com/JUGv4.png)


I always thought that a molecule couldn't be chiral if it had a plane of symmetry. Doesn't the chiral molecule here have symmetry diagonally across the OHs? 
The achiral one doesn't look symmetrical to me, so I also don't know how it is achiral. 




Regarding the **first molecule:** I understand that the simplistic Fischer projection - with all its bond depicted by solid lines - can be very confusing at first glance in determining optical activity. You may believe it to be optically inactive, hoping for a center of symmetry to exist, but it is not so.


You must keep in mind how the **molecule actually exists in 3d**! Recall the rules of Fischer projection, the horizontal bonds project outward, while the vertical bonds extend inward. Hence, the molecule would actually look like this:


[![enter image description here](https://i.stack.imgur.com/NTNKj.png)](https://i.stack.imgur.com/NTNKj.png)


Now, I hope you can tell, there is neither any center of symmetry nor any plane of symmetry here. Hence, the molecule is **chiral.**


PS: Your second molecule is chiral by similar logic, as also mentioned in the comments, and as you yourself noted.


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