#' Calculate the probability of each value of x in a partition of an event given an event y. Assuming x and y are independent.
#'
#' @param x A vector representing a partition of an event with each value representing a different possiblity (each value must be between 0 and 1 and all must add up to 1).
#' @param y The probability of the event y (values must be between 0 and 1).
#' @return A vector of the conditional probabilities of each value of x given y. The indices correspond to the indices of the vector x.
#' @examples
#' bayes_theor_extended(c(.2, .4, .4), .3)
#' @export
bayes_theor_extended = function(x, y){
if (x < 0 || x > 1) stop("Invalid probability for x!", call. = FALSE)
if (y < 0 || y > 1) stop("Invalid probabilty for y!", call. = FALSE)
if(sum(x) != 1) stop("The values of x do not add up to 1", call. = FALSE)
sum = 0
for(i in x){
sum = sum + (i * i * y)
}
prob = c(0)
count = 1
for(i in x){
prob[count] = (y * i * i) / sum
count = count + 1
}
return(prob)
}
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