I am trying to work out the probabilities of a dice system for a game I am working on.

I am rolling six sided dice (D6), and scoring a success on a 1, 2, or 3. If I roll a '1', my dice explodes - allowing me to roll a 4 sided dice (again scoring a success on a 1, 2, or 3). My D4 will not explode if I roll additional '1s'.

My working out has been: I have a 50% chance of scoring a success on the D6, and a 16.7% (rounding up) chance of that dice exploding. If it explodes I have a 75% chance of scoring a success. 16.7% of 75 = 12.525.

So the probability of rolling a success on my original D6 would be 50% + 12.5% - or 62.5% (or an average of 0.63 successes per dice, rounding up).

Is this correct? I know I have rounded up in places, but am I working this out in a way that gets me to the correct answer?

Thanks in advance for any help!