# MATHEMATICS

Consider the following contingency table.

 B Bc A 26 23 Ac 26 25

a.         Convert the contingency table into a joint probability table. (Round your intermediate calculations and final answers to 4 decimal places.)

 B Bc Total A Ac Total

b.         What is the probability that A occurs? (Round your intermediate calculations and final answer to 4 decimal places.)

Probability:

c.         What is the probability that A and B occur? (Round your intermediate calculations and final answer to 4 decimal places.)

Probability:

d.         Given that B has occurred, what is the probability that A occurs? (Round your intermediate calculations and final answer to 4 decimal places.)

Probability:

e.         Given that Ac has occurred, what is the probability that B occurs? (Round your intermediate calculations and final answer to 4 decimal places.)

Probability:

f. Are A and B mutually exclusive events?

 a. Yes because P(A | B) ≠ P(A). b. Yes because P(A ∩ B) ≠ 0. c. No because P(A | B) ≠ P(A). d. No because P(A ∩ B) ≠ 0.

g. Are A and B independent events?

 a. Yes because P(A | B) ≠ P(A). b. Yes because P(A ∩ B) ≠ 0. c. No because P(A | B) ≠ P(A). d. No becauseP(A∩B) ≠ 0.

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