Use the contingency table to the right to determine the probability of events. a

Question

Use the contingency table to the right to determine the probability of events. a. What is the probability of event A? b. What is the probability of event A'? c. What is the probability of event A and B? d. What is the probability of event A or B? a. The probability of event A is (Type an integer or decimal rounded to three decimal places as needed.) b. The probability of event A' is (Type an integer or decimal rounded to three decimal places as needed.) c. The probability of event A and B is (Type an integer or decimal rounded to three decimal places as needed.) d. The probability of event A or B is (Type an integer or decimal rounded to three decimal places as needed.)

Explanation / Answer

The row marginals are 160 and 110 respectively and column marginals are 170 and 100 respectively. Therefore, adding either the row or column marginals, the total is 270 (160+110).

a. The probability of event A is: 160/(160+110)=0.593

b. The probability of event A' is: 110/270=0.407

c. For two independent events, A and B, the probability that both A and B occur is the product of the probabilities of two events, that is P(A and B)=P(A)*P(B). The probaility of event A and B is: 160/270*170/270=0.373

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