How Can I Calculate Probabilities for Event Success Rates?

[alexbib]

I have near to no knowledge of statistics, and I want to build a statistical model that can help me calculate %chance of an event happening in situations of type:

every try has 25% success rate
after 6 tries, what are the probabilities of having succeeded at least 5times? After 12tries?

or

each shot has 42% success rate
after 5 tries, how what are the probabilities of succeding at least 4times?


How can I calculate probabilities like these?

 

[master_coda]

Sounds like you want a binomial model. Given probability of success p and n attempts, the probability of exactly k successes is:

$$\binom{n}{k}p^k(1-p)^{n-k}$$

Of course, to figure out the probability of at least k successes, you have to add up these probabilities for every value greater than or equal to k.

 

[alexbib]

what does the n above k in brackets mean?

 

[HallsofIvy]

$$\binom{n}{k}$$ is the "binomial coefficient". It is the coefficient of x^ky^n-k in (x+y)ⁿ as well as the k^th term in the n^th line in Pascal's triangle and can be calculated as $$\frac{n!}{k!(n-k)!}$$.

It is sometimes written _nC_k and our British colleagues seem to refer to it as "n choose k" since it is also the number of different ways one can choose k items from a set of n items.

 

[suyver]

And just in case you do not know what $x!$ means: it means $x$ factorial:

$$x! = 1\times 2\times 3 \times \ldots \times (x-1) \times x$$

 

[alexbib]

Ok, thanks for explanation!