SOLUTION: A is an event, and Ac is the complement of A. Which of the following statements are true? Please show work. (a) P(A AND A^C)=1 (b) P(A AND A^C = 0 © P(A OR A^C)=1 (d) P(A

Algebra ->  Probability-and-statistics -> SOLUTION: A is an event, and Ac is the complement of A. Which of the following statements are true? Please show work. (a) P(A AND A^C)=1 (b) P(A AND A^C = 0 © P(A OR A^C)=1 (d) P(A       Log On


   

Question 1029233: A is an event, and Ac is the complement of A.
Which of the following statements are true? Please show work.
(a) P(A AND A^C)=1
(b) P(A AND A^C = 0
© P(A OR A^C)=1
(d) P(A OR A^C) = 0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
P(A_or_B)=P(A)+P(B)-P(A_and_B)
So for complements,
P(A_or_Ac)=P(A)+P(Ac)-P(A_and_Ac)
However by definition of complement,
P(A_and_Ac)=0
So,
P(A_or_Ac)=P(A)+P(Ac)
P(A_or_Ac)=1
So for example, probability that it will rain or that it won't rain is 100%. _