all options

four squares, each shaded in half
join together to form a block

sometimes there are four orientations and sometimes there are only two, or one
when?

all patterns have a negative

all of the options (thanks to Puntmat for their corrections)

why are there 4^4 options altogether?

Puntmat suggest using all of the options to decide the probability of obtaining
(i) a block with a line of  symmetry (the fraction is a cube/ 7th power)
(ii) a block with reflection or rotational symmetry (of order 2 or 4)

the latter (ii) is a much neater fraction...

students could consider the ways to split a square in half and then combine these to form a 'block'
this can be coded (e.g. using: top left, top right, bottom left, bottom right)

for example...