A probability problem that you will never understand, ask for personal advice.

Maybe you should think about it this way.

Because the whole event can be divided into hit and miss, if it is only the target in fortune telling, then the sum of probabilities is definitely not 1, which is not wrong.

According to your understanding, if you want the probability to add up to 1, you should pay attention to your understanding of conditional probability, that is, the probability corresponding to the number of shots x under the condition of hitting the target. In other words, when you find the probability corresponding to different times, you need to divide it by the probability of hitting the target in the whole game, which is right.

However, I personally think that the probability of four misses should be added for the fourth time. It depends on your personal understanding.