Imagine a dangerous mountain where the chance of dying is 1%. If a group of 10 hikes the moutain, what is the probability that AT LEAST ONE of them dies? 1/100 + 1/100 + 1/100 + ... = 1/10?

Nope, a bit more complicated. The probability of someone surviving is 1-1/100. The probability that all of them survive is (1-1/100)^10. The probability that not all survive is 1 minus that 1-(1-1/100)^10.