I'm trying to solve the following homework problem:
A worker has asked her supervisor for a letter of recommendation for a new job. She estimates that there is an 80 percent chance that she will get the job if she receives a strong recommendation, a 40 percent chance if she receives a moderately good recommendation, and a 10 percent chance if she receives a weak recommendation. She further estimates that the probabilities that the recommendation will be strong, moderate, and weak are .7, .2, and .1, respectively. How certain is she that she will receive the new job offer?
I'm assuming this involves Bayes Theoerem in some manner: P(A) * P(B|A) = P(B) * P(A|B)
So I suppose P(A) could be P(getting a job), but then how would you fit into the formula the multiple types of recommendation and how that changes the probability? Would P(B) be P(getting a strong recommendation)? But then how do the other types of recommendations fit? Is this not a Bayes Theorem problem at all?