If P(BC)=0.9, find P(B). P(B)=
P(B) = 0.6, P(C) = 0.15, P(B ∩ Cc) = 0.55, and P(A ∩ Bc ∩ Cc) = 0.05. Find P(Ac ∩ Bc ∩ Cc).
Scenario 1: Suppose P(A|B)= 0.45, P(A|BC) = 0.55 and P(BC) =0.90. Using scenario 1, what is P(B)? A.10 B.41 C.50 D.61
A and B are independent P(A)=0.3 P(Ac U Bc)=0.86 What is P(B)
Let A and B be events with probabilities P(A)-3/4 and P(B)-1/3 (a) Show that 12 3' (b) Let P(AnB) - find PA n Bc).
Simplify boolean logic equation (~A~B~C)+(~A~C~D)+(AB~C)+(BC) to (AB)+(~A~B~C)+(BC)+(B~D) show steps
(a) Let P(B1∩B2)>0, and A1∪A2⊂B1∩B2. Then show that P(A1|B1).P(A2|B2)=P(A1|B2).P(A2|B1). (b) Let A and B1 be independent; similarly, let A and B2 be independent. Show that in this case, A and B1∪B2 are independent if and only if A and B1∩B2 are independent. (c) Given P(A) = 0.42,P(B) = 0.25, and P(A∩B) = 0.17, find (i)P(A∪B) ; (ii)P(A∩Bc) ; (iii)P(Ac∩Bc) ; (iv)P(Ac|Bc).
(c) Evaluate (A B)C and AT (BC) and show that they are equal. 4. Show that for any x the matrix [cos(2x) sin(2x) A= 4sin(2x) -cos(2x) Satisfies the relation A2 -I 5. Find the determinant of the following matrices:
please fast and clear Let A and B are mutually exclusive with P(BC)=1, P(AUB) Find P(A). Select one: 1/2 3/28 17/28 3/7 O 3/4
(a) If a | bc, show that a | b*gcd(a,c). (b) If a, b are coprime integers and c | at and c | bt, show that c | t. (c) If a, b, c are integers with a, c coprime, prove that gcd(ab, c) = gcd(b, c).