# Probability of target shooting question

• pixel01
In summary, the conversation involves a man trying to determine the number of shots he needs to take to have a 95% success rate in shooting a target with a 30% probability of success. The suggested solution involves using the formula P = p^n + p^(n-1)*q + p^(n-2)*q^2 + ... + p*q(n-1) where q=1-p, and the first term in the expansion represents the probability of all n shots being successful. However, more steps may be needed to shorten the result.
pixel01
Hi all,

It's rather long time I haven't dealt with maths. Now I have this problem.
A man can shoot right on the target with the probability of success of p = 30%. The question is how many shots does he need to shoot to be 95% (P) successful.

My idea is :
Let n the number of shots needed. Then P = p^n+p^(n-1)*q+p^(n-2)*q^2...+p*q(n-1)
where q=1-p.
Am i right and if yes, how can I shorten the result?

Thanks for any help.

In the expansion p^n + n*p^(n-1) +++q^n, it is the first term that tells us the probability that all of the n shots would be successful. The next term tells us of one failue and n-1 successes. But those terms are not what we are looking for. So I think that's a start on the problem.

Last edited:

## 1. What is the probability of hitting the target in a single shot?

The probability of hitting the target in a single shot depends on various factors such as the distance of the target, the size of the target, and the skill of the shooter. It is impossible to determine a specific probability without knowing all of these factors.

## 2. How can I calculate the probability of hitting the target in multiple shots?

The probability of hitting the target in multiple shots can be calculated by multiplying the individual probabilities of hitting the target in each shot. For example, if the probability of hitting the target in a single shot is 0.5, the probability of hitting the target in two shots would be 0.5 x 0.5 = 0.25.

## 3. Is the probability of hitting the target the same for all shooters?

No, the probability of hitting the target can vary for different shooters. It depends on their skill level, experience, and factors such as their physical and mental condition at the time of shooting.

## 4. Can the probability of hitting the target be improved?

Yes, the probability of hitting the target can be improved through practice and training. The more familiar a shooter is with their equipment and the better their shooting technique, the higher their chances of hitting the target.

## 5. How can I use probability to improve my target shooting skills?

Understanding probability can help shooters to set realistic expectations and goals for themselves. It can also help them to analyze their performance and identify areas for improvement. Additionally, knowing the probability of hitting the target in different scenarios can help shooters make more informed decisions during competitions or hunting trips.

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