I am just starting out about learning about Bayes' theorem. The statement that I am calculating for is "I received an email, what is the probability that it is spam given that the email contains the work 'Nigeria'?". I assume that of all email messages 80% are spam and 20% are not.
W represents that percentage of emails that are not spam L denotes that the email contains the word 'Nigeria'
P(W) = 0.8 (percent of email that is spam)
P(M) = 0.2 (percent of email that is not spam)
P(L|W) = 0.95 (percent of all spam emails that have the word Nigeria in them)
P(L|M) = 0.1 (percent of all non spam emails that have the word Nigeria in them)
So solving: $$P(W|L) = {P(L|W)* P(W) \over P(L|W) * P(W) + P(L|M) * P(M)}$$
I get P(W|L) = 0.974359
Is this correct (I am asking because I want to confirm that my understanding of the this concept is correct)?
P.S. - If updated the example in this question to an example that I think is more appropriate to the theorem.
Your answer is correct up to the digits you give. In mathematics, the equality sign is usually reserved for exact equalities, and approximate equalities, e.g. after rounding, are denoted by $\approx$.