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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