Suppose PA 6 PB 4 and PAB 5 Note PA B does not equal 1 a

Suppose P(A) = .6, P(B) = .4 and P(A|B) = .5. Note, P(A B) does not equal 1

(a) Find P(A B)

(b) Find P(A^c B^c )

Please show all process

Solution

a)

P(A|B) = .5. => P( A n B)/ P(B) = 0.5 => P(A n B) = 0.5 * 0.4 = 0.20

b)

P( A u B) = 0.6 + 0.4 - 0.20 = 0.80

P(Ac Bc ) = Compliment of  P(A n B) = 1 - 0.20 = 0.80