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 ?
A speaks truth in 60% of the cases, while B in 90% of cases. In what percent of cases are they likely to contradict each other in stating the same fact ? In the cases of contradiction do you think, the statement of B will carry more weight as he speaks truth in more number of cases than A ?
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 alternately. A wins the game if he gets a total of 7 and B wins the game if he gets a total of 10. If A starts the game, then find the probability that B wins.
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.
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 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.
Let f : X -> Y be a function. Define a relation R on X given be R = {(a, b) : f(a) = f(b)}. Show that R is an equivalence relation ?
If Z is the set of all integers and R is the relation on Z defined as R = {(a, b) : a, b ∈ Z and a – b is divisible by 5}. Prove that R is an equivalence relation.
Let A = R – {2}, B = R – {1}. If f : A → B is a function defined by show that f is one-one and onto. Hence find
Sand is pouring from the pipe at the rate of 12 cm³/s. The falling sand forms a cone on a ground in such a way that the height of cone is always one-sixth of radius of the base. How fast is the height of sand cone increasing when the height is 4 cm ?