Almost every case of what appears random to us is due to not knowing enough about the situation. For example, when you flip a coin, you don't know exactly how you flipped it (how much force you applied, how fast it will rotate, how it left your hand, air currents, etc.) If you did know all this, it wouldn't be random: you could predict whether it would land heads or tails. Because you don't know any of this, it seems random.

The same goes for computers, only moreso. They use complex algorithms to generate "random" numbers, but if you know exactly how these algorithms work, you can predict the numbers.

The only place I know of that truly has randomness is the quantum world. If you have a particle that has a 50/50 chance of being in state A or B, no amount of information will tell you which state it's in before measuring it.

As for choosing a banana, who knows? No one knows how consciousness really works, so no one can say whether there's randomness involved or not.