From the differential equation of equation y = a cos 2x + b sin 2x, where a and b are constant.
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).
One bag contains 3 red and 5 black balls. Another bag contains 6 red and 4 black balls. A ball is transferred from first bag to the second bag and then a ball is drawn from the second bag. Find the probability that the ball drawn is red.
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(E) = 7/13, P(F) = 9/3 and P(E' / F') = 4/3, then evaluate :
(i) P(E / F)
(ii) P(E / F)
If P(E) = 6/11, P(F) = 5/11 and P(E ∪ F) = 7/11 then find
(i) P(E/F)
(ii) P(F/E)
Obtain the differential equation of the family of circles passing through the points (a, 0) and (– a, 0).