You are enrolled in MBA 440. At the beginning of the semester, you used your hunch to estimate the likelihood of passing this class. Let P be the event of passing the class; F is the event of failing the class. Your prior probabilities are as follows: P(P)=0.7 P(F)=0.3
You are enrolled in MBA 440. At the beginning of the semester, you used your hunch to estimate the likelihood of passing this class. Let P be the
P(P)=0.7
P(F)=0.3
After the first week of class, you find out that you have failed the first assignment. Let A1 be the event of passing the first assignment; let A2 be the event of failing the first assignment. Now you feel you need to update your belief about the likelihood of passing this class. You talk to your Professor and she tells you that given someone has passed the class, the probability of passing the first assignment is 0.8, i.e. P(A1|P)=0.8. She also gives you the following conditional probabilities:
P(A2|P)=0.2; P(A1|F)=0.3 and P(A2|F)=0.7.
What is the posterior probability that you will pass this class given that you have failed the first assignment?
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