# Question: The prior probabilities for events A1 A2 and A3 are

The prior probabilities for events A1, A2, and A3 are P(A1) = .20, P(A2) = .50, and P(A3) = .30. The conditional probabilities of event B given A1, A2, and A3 are P(B | A1) 5 .50, P(B | A2) = .40, and P(B | A3) = .30.

a. Compute P(B ( A1), P(B ( A2), and P(B ( A3).

b. Apply Bayes’ theorem, equation (4.19), to compute the posterior probability P(A2| B).

c. Use the tabular approach to applying Bayes’ theorem to compute P(A1| B), P(A2| B), and P(A3| B).

a. Compute P(B ( A1), P(B ( A2), and P(B ( A3).

b. Apply Bayes’ theorem, equation (4.19), to compute the posterior probability P(A2| B).

c. Use the tabular approach to applying Bayes’ theorem to compute P(A1| B), P(A2| B), and P(A3| B).

## Relevant Questions

In August 2012, tropical storm Isaac formed in the Caribbean and was headed for the Gulf of Mexico. There was an initial probability of .69 that Isaac would become a hurricane by the time it reached the Gulf of Mexico ...A study of 31,000 hospital admissions in New York State found that 4% of the admissions led to treatment-caused injuries. One-seventh of these treatment-caused injuries resulted in death, and one-fourth were caused by ...The five most common words appearing in spam emails are shipping!, today!, here!, available, and fingertips! (Andy Greenberg, “The Most Common Words In Spam Email,” Forbes website, March 17, 2010). Many spam filters ...Consider a Poisson distribution with μ = 3.a. Write the appropriate Poisson probability function.b. Compute f(2).c. Compute f(1).d. Compute P(x $ 2).A technician services mailing machines at companies in the Phoenix area. Depending on the type of malfunction, the service call can take 1, 2, 3, or 4 hours. The different types of malfunctions occur at about the same ...Post your question