Air Admittance?

[leescortxr3i]

Hi all. A quick question on a bit of plumbing I'm putting together please. I've a sink and a shower waste that are emptying into the same run of 40mm waste pipe which runs under the floor and to the outside. I was thinking, to avoid any gurgling, I'll put a waste trap with an auto/built-in vent onto the sink, but do I need one on the shower waste? I've put a diagram of the layout below if it helps. My options with the shower waste are limited as I'm using an Impey waste trap which came with my shower tray and it doesn't have a vent built in. But not entirely sure if I need one? Would water flowing from the sink pull the water from the shower trap if there's a vent on the sink waste? Would it pull in air there in preference to pulling the shower waste water in the trap?

Shower waste:

Any advice would be appreciated. Many thanks.
Lee

 

[denso13]

You don't have many options, one on the basin only should be ok.