Probability Tes...

A man has $$3$$ coins $$A, B$$ & $$C$$. $$A$$ is fair coin. $$B$$ is biased such that the probability of occurring head on it is $$2/3$$. $$C$$ is also biased with the probability of occurring head as $$1/3$$. If one coin is selected and tossed three times, giving two heads and one tail, find the probability that the chosen coin was $$A$$

Let $$A$$ and $$B$$ be two events such that $$P(\overline { A\cup B } )=\cfrac { 1 }{ 6 } ,P(A\cap B)=\cfrac { 1 }{ 4 } $$ and $$P(\overline { A } )=\cfrac { 1 }{ 4 } $$, where $$\overline { A } $$ stands for complement of event $$A$$. Then, the events $$A$$ and $$B$$ are

If two events $$A$$ and $$B$$ are such that $$P({ A }^{ c })=0.3\quad $$ and $$P(B)=0.4$$ and $$P\left( { A\cap B } \right)^c =0.5$$, then $$P\left[ B|\left( A\cup { B }\right)^c  \right] $$ is equal to

The probabilities of three mutually exclusive events A, B and C are given by $$\frac{1}{3}, \frac{1}{4}$$, and $$\frac{5}{12}$$. Then $$(P \cup B \cup C)$$ is.

If $$\dfrac {1 + 3p}{3}, \dfrac {1 - p}{4}$$ and $$\dfrac {1 - 2p}{2}$$ are mutually exclusive events. Then, range of $$p$$ is

Probability of any event $$x$$ lies

Let A and B be any two events and S be the corresponding sample space. Then $$P(\bar{A}\cap B)$$

If $$\frac{1+4p}{p};\frac{1-p}{4};\frac{1-2p}{2}$$ are probabilities of three mutually exclusive events, then the possible values of $$'p'$$ belong to the set is..

There are eight delegates $$4$$ of them are Americans, $$1$$ British, $$1$$ Chinese, $$1$$ Dutch and $$1$$ Egyptian. These delegates are paired randomly.The probability that no two delegates of the same country are paired is

Consider the following events.
$$E_1$$: Six fair dice are rolled and at least one die shows six.
$$E_2$$: Twelve fair dice are rolled and at least two dice show six.
Let $$p_1$$ be the probability of $$E_1$$ and $$p_2$$ be the probability of $$E_2$$. Which of the following is true?