Similarly, if we wanted to know the joint probability of an entire sequence of words like its water is so transparent, we could do it by asking "out of all possible sequences of five words, how many of them are its water is so transparent?" We would have to get the count of its water is so transparent and divide by the sum of the counts of all possible five word sequences. That seems rather a lot to estimate! For this reason, we'll need to introduce more clever ways of estimating the probability of a word w given a history h, or the probability of an entire word sequence W . Let's start with a little formalizing of notation. To represent the probability of a particular random variable X i taking on the value "the", or P(X i = "the"), we will use the simplification P(the). We'll represent a sequence of N words either as w 1 . . . w n or w 1:n (so the expression w 1:n−1 means the string w 1 , w 2 , ..., w n−1 ). For the joint probability of each word in a sequence having a particular value P(X = w 1 ,Y = w 2 , Z = w 3 , ...,W = w n ) we'll use P(w 1 , w 2 , ..., w n ).