Based on the following data, what is the probability of a person making no error in her tax returns without support from a tax advisor?
50% of individuals get help from a tax advisor to file their returns. The probability of an individual making an error in the tax return is 25%. The chance of the person making an error, given a tax advisor is helping, is 10%.
Let P(M|A) be the probability of not making the error, given an advisor is not helping.
Based on the Conjunction Rule,
P(M & A) = P(A) x P(M|A)
P(M|A) = P(M & A) / P(A)
P(A) = probability of no advisor
P(M & A) = joint probability of no error AND no advisor.
