Prove that if E and F are independent events, then the events E and F' are also independent.
If E and F are two events such that P(E) = 1/4, P(F) = 1/2 and P(E ∩ F) = 1/8, find
(i) P(E or F)
(ii) P(not E and not F).
If E and F be two events such that P(E) = 1/3, P(F) = 1/4, find P(E U F) if E and F are independent events.
If A and B are two events such that P(A) = 0.4, P(B) = 0.8 and P(B/A) = 0.6, then find P(A/B).
A die is rolled. If E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5}, find
(a) P(E U F)/G]
(b)P [(E ∩ F)/G].
If A and B are two independent events, then prove that the probability of occurrence of at least one of A and B is given by 1 – P(A’) · P(B’)
If P(F) = 0·35 and P(E U F) = 0·85 and E and F are independent events. Find P(E).
From the differential equation of equation y = a cos 2x + b sin 2x, where a and b are constant.
Verify that ax² + by² = 1 is a solution of differential equation
How many equivalence relations on the set {1, 2, 3} containing (1, 2) and (2, 1) are there in all ?Justify your answer.