Why don't positrons annihilate with electrons in a cloud chamber?

I'm pretty sure they do. Just not necessarily with the first electron the come close to. If I remember correctly, the probability of an electron and a positron annihilating with each other when they meet (whatever "meeting" may mean exactly for elementary particles) decreases with their relative velocity (or equivalently: relative momentum). So very fast positrons may (and apparently do) survive some distance before they react with electrons and vanish.

Thanks timo