If E and F are independent events, then show that
(i) E and F' are independent events.
(ii) E' and F are also independent events.
(i) E and F' are independent events.
(ii) E' and F are also independent events.
Prove that if E and F are independent events, then the events E and F' are also independent.
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 independent events such that P(A' ∩ B)= 2/15 and P(A ∩ B')= 1/6, then find P(A) and P(B).
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 particle moves along the curve 6y = x³ + 2. Find the points on the curve at which y-coordinate is changing 2 times as fast as x-coordinate.
The radius r of the base of a right circular cone is decreasing at the rate of 2 cm/min. and height h is increasing at the rate of 3 cm/min. When r = 3.5 cm and h = 6 cm, find the rate of change of the volume of the cone.
Find the differential equation of the family of curves y²= 4ax.
A box contains 50 bolts and 50 nuts. Half of the bolts and nuts are rusted. If two items are drawn with replacement, what is the probability that either both are rusted or both are bolts.
The radius r of a right circular cone is decreasing at the rate of 3 cm/minute and the height h is increasing at the rate of 2 cm/minute. When r = 9 cm and h = 6 cm, find the rate of change of its volume.