SOLUTION: A and B are the two events in S, and P(A)=0.9 and P(B)=0.6 a) Is it possible that P(A ∩ B) = 0.77? Why or why not? b) What is the largest possible value for P(A ∩ B)?

Algebra ->  Probability-and-statistics -> SOLUTION: A and B are the two events in S, and P(A)=0.9 and P(B)=0.6 a) Is it possible that P(A ∩ B) = 0.77? Why or why not? b) What is the largest possible value for P(A ∩ B)?       Log On


   

Question 1170102: A and B are the two events in S, and P(A)=0.9 and P(B)=0.6
a) Is it possible that P(A ∩ B) = 0.77? Why or why not?
b) What is the largest possible value for P(A ∩ B)?
Answer by ikleyn(52808) About Me  (Show Source):
You can put this solution on YOUR website!
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(a)  Is it possible that P(A ∩ B) = 0.77? Why or why not?


     ANSWER.  It is not possible.


     Explanation.  P(A ∩ B)  CAN NOT be more than P(A)  or  P(B).

                   ( it is obvious . . . and everybody must know it . . . )




(b)  What is the largest possible value for P(A ∩ B)?


     ANSWER.  The largest possible value for  P(A ∩ B)  is  min(P(A),P(B)),  which is 0.6 in this case.

              ( it is obvious . . . and everybody must know it . . . )


Solved, explained and completed.