`P'(E)=1-P(E)`

Let A and B be two independent events. Statement-1: If P(A)=0.3 and P(A cup overline(B))=0.8 , then P(B)=(2)/(7) Statement-2: For any event E, P(overline(E ))=1-P(E ) .

If E and F are two events such that P(E)=1/4, P(E)=1/2 and P(E and F)=1/8 . Find P (not E and not F).

A sample space consists of 9 elementary outcomes E1, E2, ..., E9 whose probabilities are P(E1) = P(E2) = 0.08, P(E3) = P(E4) = P(E5) = 0.1 P(E6) = P(E7) = 0.2, P(E8) = P(E9) = 0.07 SupposeA = {E1, E5, E8}, B = {E2, E5, E8, E9} (a) Calculate P (A), P (B), and P (A ∩ B) (b) Using the addition law of probability, calculate P (A ∪ B) (c) List the composition of the event A ∪ B, and calculate P (A ∪ B) by adding the probabilities of the elementary outcomes. (d) Calculate P (Bar B) from P

Let A, B,C be any three events in a sample space of a random experiment. Let the events E_(1)= exactly one of A,B occurs, E_(2)= exactly one of B ,c occurs, E_(3)= exactly one of c ,A occurs, E_(4)= all of A,B ,c occurs, E_(5)= atleast one of A,B, c occurs P(E_(1))=P(E_(2))=P(E_(3))=(1)/(3),P(E_(4))=1/9,P(E_(5))=

If E_1 and E_2 are two independent events associated with an experiment, then show that P(E_1cupE_2)=1-P(E_1^c)P(E_2^c)

A sample space consists of 9 elementary outcomes E_(1),E_(2),…..,E_(9) whose probabilities are P(E_(1))=P(E_(2))=0.08,P(E_(3))=P(E_(4))=P(E_(5))=0.1 P(E_(6))=P(E_(1))=0.2,P(E_(8))=P(E_(9))=0.07 "Suppose"" "A={E_(1),E_(5),E_(8)},B={E_(2),E_(5),E_(8),E_(9)} (i) Calculate P(A), P(B) and P(AcapB) . (ii) Using the addition law of probability, calculate P (AcupB). (iii) List the composition of the event AcupB and calculate P(AcupB) by adding the probabilities of the elementary outcomes. Calculate P(overset(-)B) from P(B), also calculate P(overset(-)B) directly from the elementary outcomes of overset(-)B ,

A sample space consists of 9 elementary outcomes E_(1),E_(2),…..,E_(9) whose probabilities are P(E_(1))=P(E_(2))=0.08,P(E_(3))=P(E_(4))=P(E_(5))=0.1 P(E_(6))=P(E_(1))=0.2,P(E_(8))=P(E_(9))=0.07 "Suppose"" "A={E_(1),E_(5),E_(8)},B={E_(2),E_(5),E_(8),E_(9)} (i) Calculate P(A), P(B) and P(AcapB) . (ii) Using the addition law of probability, calculate P (AcupB). (iii) List the composition of the event AcupB and calculate P(AcupB) by adding the probabilities of the elementary outcomes. Calculate P(overset(-)B) from P(B), also calculate P(overset(-)B) directly from the elementary outcomes of overset(-)B ,

Statement -1 : Let E_1, E_2, E_3 be three events such that P(E_1)+P(E_2)+P(E_3)=1, " then " E_1, E_2, E_3 are exhaustive events. Statement-2 if the events E_1, E_2 " and " E_3 be exhaustive events, then P(E_1cupE_2cupE_3)=1

Statement -1 : Let E_1, E_2, E_3 be three events such that P(E_1)+P(E_2)+P(E_3)=1, " then " E_1, E_2, E_3 are exhaustive events. Statement-2 if the events E_1, E_2 " and " E_3 be exhaustive events, then P(E_1cupE_2cupE_3)=1

Let E and F be two events such that P(E)=(1)/(4),P(E|A)=(1)/(2) and P(F|E)=(1)/(2). Then P(F|E^(C)) is