Mathematicians and politicians throughout history have dueled.

Alexander Hamilton and Aaron Burr dueled.

The French mathematician Evariste Galois died in a duel.

Consider two individuals (H) and (B) for example dueling.

In each round they simultaneously shoot the other and the probability

of a fatal shot is \(0 < p < 1\).

1) What is the probability they are fatally injured in the same round ?

2) What is the probability that (B) will be fatally injured before (H) ?