Yes, I agree the probability of both being successful is 6.25%....

Yes, I agree the probability of both being successful is 6.25%. I also stand by what I wrote.

We have 2 wells, call them A and B. If we think 'binary', i.e. a well is duster/unsuccessful (probability 75%) or gusher/successful (prob 25%), (and we all know that in reality there are many outcomes in between) there are 4 possible outcomes:

1. A & B both gushers.
2. A is gusher, B is duster
3. A is duster, B is gusher
4. A & B both dusters.

Chance of outcome 1 is 25% x 25% = 6.25%
Chance of outcome 2 is 25% x 75% = 18.75%
Chance of outcome 3 is 75% x 25% = 18.75%
Chance of outcome 4 is 75% x 75% = 56.25%

Outcomes 1, 2 and 3 each have 'at least one successful' well. Sum of probabilities for 1, 2 and 3 = 43.75%. Which is what I said. Maybe the application of my maths to oil drilling is a bit simplistic, but I still claim the maths is rigorous.

As shareholders, if either one of those wells hits paydirt, so do we!