A and B throw a pair of dice alternately. A wins the game if he gets a total of 9 and B wins if he gets a total of 7. If A starts the game, find the probability of winning the game by B.
A and B throw a pair of dice alternatively, till one of them gets a total of 10 and wins the game. Find their respective probabilities of winning, if A starts first.
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.
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.
P speaks truth in 70% of the cases and Q in 80% of the cases. In what percent of cases are they likely to agree
in stating the same fact ?
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’)
Prove that if E and F are independent events, then the events E and F' are also independent.
Find the equation of tangent to the curve 4x² + 9y² = 36 at the point (3 cos θ, 2 sin ).
Let f : N → R be a function defined as f(x) = 4x² + 12x + 15. Then show that f : N → S, where S is range of f, is invertible. Also find the inverse of f.
Find the equation of tangents to the curve y = x³ + 2x – 4 which are perpendicular to the line x + 14y – 3 = 0.
Find the equations of the normal to the curve x² = 4y which passes through the point (1, 2).