(Solved): need help on d. and e. Consider the following contingency table. a. Convert the contingency table in ...

Consider the following contingency table. a. Convert the contingency table into a joint probability table. (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.) b. What is the probability that A occurs? (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.) c. What is the probability that \( A \) and \( B \) occur? (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.) d. Given that \( B \) has occurred, what is the probability that \( A \) occurs? (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.) e. Given that \( A^{C} \) has occurred, what is the probability that \( B \) occurs? (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.) f. Are \( A \) and \( B \) mutually exclusive events? Yes because \( P(A \mid B) \neq P(A) \). Yes because \( P(A \cap B) \neq 0 \). No because \( P(A \mid B) \neq P(A) \). No because \( P(A \cap B) \neq 0 \). 9. Are \( A \) and \( B \) independent events? Yes because \( P(A \mid B) \neq P(A) \). Yes because \( P(A \cap B) \neq 0 \). No because \( P(A \mid B) \neq P(A) \).