If `E_(1)` and `E_(2)` are two independent events, then `P(E_(1)nn E_(2))` is equal to

If E and F are independent events, then write P (E uu F)

Let E_(1) and E_(2) be two independent events such that P(E_(1))=P_(1) and P(E_(2))=P_(2) , describe in words of the events whose probabilities are (i) P_(1)P_(2) (ii) (1-P_(1))P_(2) (iii) 1-(1-P_(1))(1-P_(2)) (iv) P_(1)+P_(2)-2P_(1)P_(2)

For any two independent events E_1 and E_2 P{(E_1uuE_2)nn(bar(E_1)nnbar(E_2)} is equal to

If E\ a n d\ E_2 are independent events, write the value of P(E_1uuE_2)nn( E_c1nn Ec_2)dot

If E_(1) and E_(2) are two events such that P(E_(1))=1//4 , P(E_(2)//E_(1))=1//2 and P(E_(1)//E_(2))=1//4 , then

If E and F are two independent events and P(E)=1/3,P(F)=1/4, then find P(EuuF) .

If E_(1) and E_(2) be two events such that P(E_(1))=0.3, P(E_(2))=0.2 and P(E_(1)nnE_(2))=0.1, then find: (i) P(barE_(1)nnE_(2)) (ii) P(E_(1)nnbarE_(2))

A and B are two events defined as follows: A:It rains today with P(A)=40 % B: It rains tomorrow with P(B)=50 % Also, P (it rains today and tomorrow) =30 % Also, E_1: P(AnnB)//(AuuB) and E_2: P({(Ann barB )or(Buu barA )}//(AuuB)) . Then which of the following is/are true ? (a) A and B are independent events (b) P(A//B) (c) E_1 and E_2 are equiprobable (d) P(A/(AuuB))=P(B//(AuuB))

If E and F are independent events such that 0 < P(E) < 1 and 0 < P(F) < 1, then (a) E and F are mutually exclusive (b) E and F^c (the complement of the event F ) are independent (c) E^c and F^c are independent (d) P(E//F)+P(E^c//F)=1

Let E_(1) and E_(2) be two ellipse whsoe centers are at the origin. The major axes of E_(1) and E_(2) lie along the x-axis , and the y-axis, respectively. Let S be the circle x^(2)+(y-1)^(2)=2 . The straigth line x+y=3 touches the curves, S, E_(1) and E_(2) at P,Q and R, respectively . Suppose that PQ=PR=(2sqrt(2))/(3) . If e_(1) and e_(2) are the eccentricities of E_(1) and E_(2) respectively, thent hecorrect expression (s) is (are)