Probability Tes...

Let $$A$$ and $$B$$ are events of an experiment and $$P(A)=\dfrac 14,  P(A \cup B) = \dfrac 12$$, then value of $$ P(\dfrac B{A^c}) $$ is

There are 10 pairs of shoes in a cupboards, from which 4 shoes are picked at random. The probability that there is at least one pair, is..........

Three groups $$A,\ B,\ C$$ are contesting for positions on the Board of Directors of a company. The probabilities of their winning are $$0.5,\ 0.3, 0.2$$ respectively. If the group $$A$$ wins, the probability of introducing a new product is $$0.7$$ and the corresponding probabilities for groups $$B$$ and $$C$$ are $$0.6$$ and $$0.5$$ respectively. The probability that the new product will be introduced is given by

A box contains $$100$$ tickets numbered $$1,2,3,...,100.$$ two tickets are chosen at random. If it is given that the maximum number on the two chosen tickets is not more than $$10$$, then the probability that the minimum number on them is not less than $$5$$ is

A box contains $$100$$ tickets numbered $$1,2,.....100$$. Two tickets are chosen at random. It is given that the minimum number on the two chosen tickets is not more than $$10$$. The maximum number on them is $$5$$ with probability.

An experiment has $$10$$ equally likely outcomes. Let $$A$$ and $$B$$ be two non-empty events of the experiment. If $$A$$ consists of $$4$$ outcomes, the number of outcomes that $$B$$ must have so that $$A$$ and $$B$$ are independent, is

If $$\overline { E } $$ and $$\overline { F } $$ are the complementary events of events $$E$$ and $$F$$ respectively and if $$0<P(F)<1$$, then

A man is known to speak the truth $$3$$ out of $$4$$ times. He throws a die and reports that it is a six. The probability that it is really a six is

Suppose $$n(\ge 3)$$ persons are sitting in row. Two of them are selected at random. The probability that they are not together is

Let $$A = {2, 3, 4, ... , 20, 21}$$. A number is chosen at random from the set $$A$$ and it is found to be a prime number. The probability that it is more than $$10$$ is