Consider the following joint probability table B1 B2 B3 B4 A

Consider the following joint probability table B1 B2 B3 B4 A 0.13 0.10 0.09 00.11 AC 0.13 0.12 0.17 0.15 Click here for the Excel Data File a. What is the probability that A occurs? (Round your answer to 2 decimal places.) Probability b. What is the probability that B2 occurs? (Round your answer to 2 decimal places.) Probability c. What is the probability that AC and B4 occur? (Round your answer to 2 decimal places.) Probability d. What is the probability that A or B3 occurs? (Round your answer to 2 decimal places.) Probability e. Given that B2 has occurred, what is the probability that A occurs? (Round your intermediate calculations and final answers to 4 decimal places.) Probability f. Given that A has occurred, what is the probability that B4 occurs? (Round your intermediate calculations and final answers to 4 decimal places.) Probability

Solution

A)

P(A) = 0.13+0.10+0.09+0.11 = 0.43 [answer]

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b)

P(B2) = 0.10+0.12 = 0.22 [answer]

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c)

P(Ac and B4) = 0.15 [answer]

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d)

P(A or B3) = 0.13+0.10+0.09+0.11+0.17 = 0.60 [answer]

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e)

P(A|B2) = P(A and B2) / P(B2) = 0.10/(0.10+0.12)

= 0.454545455 [answer]

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f)

P(B4|A) = P(B4 and A) / P(A) = 0.11/0.43 = 0.255813953 [answer]