[ArizonaJim]

rajahamsa

A salesman can tell a customer almost anything about the life of a tyre (or anything else) and later claim he was only making an estimate.
Don't believe them.
Instead, rely on your own eyes to see if there is sufficient tread left to provide good grip on the road and to displace water on rainy days.

The very shallow. worn tread grooves on your tyres can do neither of these things reliably.

The rubber which tires are made from also is effected by the weather and over a few years, the rain, suns ultraviolet radiation and the ozone in the air will reduce its flexibility and grip making it harder and more likely to skid.

For your and your families safety you need to spend some money and replace both of your tyres.

Even the best of tyres will skid on a road with loose dirt, mud or rain on it.
When riding with any of those conditions, heighten your awareness of everything around you so you can be ready to make a evasive move or stop suddenly.

I won't go into using the front brake as others have mentioned that except to say the fastest motorcycle riders in the world rely primarily on their front brakes to do over 80 percent of their braking with the rear brake picking up the remaining 20 percent. A good rider should learn from them and do the same.