Senior high school mathematics problems (independent repeated test) 1. Assuming that the probability of event a occurring at least once in four independent repeated experiments is 80 / 81, try to find the probability of event a occurring in another experiment 2. Someone shoots at a target until it is hit. The probability of each shot hitting the target is 1 / 3. Calculate the probability of hitting the target for the nth time

Senior high school mathematics problems (independent repeated test) 1. Assuming that the probability of event a occurring at least once in four independent repeated experiments is 80 / 81, try to find the probability of event a occurring in another experiment 2. Someone shoots at a target until it is hit. The probability of each shot hitting the target is 1 / 3. Calculate the probability of hitting the target for the nth time

1. Let the probability of occurrence be X
The probability of at least one occurrence is 80 / 81
So the probability of not happening is one in 81
The probability of not happening four times is (1-x) ^ 4 = 1 / 81
x=2/3
Stop because it hits
So the first n-1 times didn't hit, the nth time hit
The probability is (2 / 3) ^ (n-1) * 1 / 3