building a statistical model

[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 xkyn-k in (x+y)n as well as the kth term in the nth line in Pascal's triangle and can be calculated as \frac{n!}{k!(n-k)!}.

It is sometimes written nCk 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, thx for explanation!