Question about the Division operator in R not returning the correct value

Question

I am trying to caculate the Bayes Theorem for Cancer and tried to plug in the correct values in my formula as such:

cancer <- (1 * (1/100000)) / (1*(1/100000)) + ((10/99999) * (99999/100000))

In this case, cancer = 1.0001

However, the correct answer should be: 0.09090909, as proven by running the code separately, like this:

num = (1 * (1/100000))
den = (1*(1/100000)) + ((10/99999) * (99999/100000))

num / den

> 0.09090909

Can you please let me know why this is the case and how I should run the combined equation in the future to get the proper result?

Answer 1

Parentheses are needed:

cancer <- (1 * (1/100000)) / ((1*(1/100000)) + ((10/99999) * (99999/100000)))