Soya you had misundertood,actually the less tread means more grip because more contact on the road(in same quality and age). Tread on tires is to channel or evacuate the water away to avoid aqua-planning(aquaplanning means your tires floating on the water,no contact on the road,means you have no/lost control for the grip). Tread on tires also used to improve grip on muddy or loose dirt road,that is why off-road 4x4 car need bigger tread during drive on off-road.

Why new tires at behind? If old tires at behind when cornering if you lost control at back,everything is too late for average driver,when you realize and the car already spin.
Now if anything went wrong in front,your steering would shake and warning you very early there is something wrong with the grip,and you still can maintain control with the steering. But if behind? You have nothing to control.
If you really concern your safety,just change all 4 of your tires. Then there is no more argument. If not then just don't speeding and stay sensible speed. Driving need lots of experience and attention.

Ah.. another thing is really important,correct air pressure in your tires play important role too,result stable ride,control,grip safety,save from tire explode,save petrol,etc. Most of Malaysian driver  seldom check air pressure until something went wrong and blame the tires no good la bla bla bla. Believe me,ask them driver what is their cars correct air pressure. How many PSI/BAR?
Some of them also use the air pump in the station wrongly,they simply just inflate pressed the wrong button(button to inflate punctured tire,the pump inflate to the maximum!) and drive away. How much air? They said it doesn't matter as long as can run then mo problem.