Correct drain plumbing( pic attached)

[Supperfly17]

I moved into a house and this is how the sink/washing machine drain looks like. Does this look correct?
My wife finds that she has to have the sink closed from top in order for it to smell less when she is washing clothes. Any help is appreciated.

 

[Terry]

Smells less? I wonder what is back in the wall where the vent should be. Normal plumbing would have a vent to break the siphon on the p-trap when water is being drained down it to keep a water seal to prevent smells and gas from coming up.

What you have looks pretty odd. A washer p-trap and standpipe are 2" and it looks like you might have 1-1/2" going into the wall. Do you know if the trap there is siphoning? That would be your smell, and if so adding an AAV before the wall would help.