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).
The length x, of a rectangle is decreasing at the rate of 5 cm/minute and the width y, is increasing at the rate of 4 cm/minute. When x = 8 cm and y = 6 cm, find the rate of change of the area of the rectangle.
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.
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].
A balloon, which always remains spherical, has a variable diameter . Find the rate of change of its volume with respect to x.
If P(F) = 0·35 and P(E U F) = 0·85 and E and F are independent events. Find P(E).
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)
A couple has 2 children. Find the probability that both are boys, if it is known that
(i) one of them is a boy
(ii) the older child is a boy.