Hi everyone,

I am trying to model a french vocabulary test, finding the probability of passing, based on a number of factors.

Currently, I am looking at Binomial Distribution and Poisson Binomial Distribution of Bernoulli trials.

The way I am separating my data is based on connection to the English language and word length. My data is coming from previous tests I have done. What I am trying to do is combine the passing probability of different sets of types of words, to find an overall probability.

For Example,and combining this with another set of words.

Word length of 5, unrelated-to-English Pass/fail belle pass chaid fail santé pass avoir pass

I think that poisson binomial distribution is the more likely one but I dont know how to apply the formula:

The probability of havingksuccessful trials out of a total ofncan be written as the sum^{[1]}

{\displaystyle \Pr(K=k)=\sum \limits _{A\in F_{k}}\prod \limits _{i\in A}p_{i}\prod \limits _{j\in A^{c}}(1-p_{j})}where {\displaystyle F_{k}} is the set of all subsets ofkintegers that can be selected from {1,2,3,...,n}. For example, ifn= 3, then {\displaystyle F_{2}=\left\{\{1,2\},\{1,3\},\{2,3\}\right\}}. {\displaystyle A^{c}} is the complement of {\displaystyle A}, i.e. {\displaystyle A^{c}=\{1,2,3,\dots ,n\}\setminus A}.