If the events A and B are mutually exclusive events such that $$P(A)=\frac{1}{3}(3 x+1)$$ and $$P(B)=\frac{1}{4}(1-x)$$ then the possible values of $x$ lies in the interval
An urn contains 2 white and 2 black balls. A ball is drawn at random. If it is white it is not replaced into the urn. Otherwise it is replaced along with another ball of the same colour. The process is repeated. The probability that the third ball drawn is black is
A random variable X with probability distribution is given below
| $$ \mathrm{X}=x_i $$ |
2 | 3 | 4 | 5 |
|---|---|---|---|---|
| $$ \mathrm{P}\left(\mathrm{X}=x_i\right) $$ |
$$ \frac{5}{k} $$ |
$$ \frac{7}{k} $$ |
$$ \frac{9}{k} $$ |
$$ \frac{11}{k} $$ |
The mean of this distribution is
A number $$\mathrm{n}$$ is chosen at random from $$s=\{1,2,3, \ldots, 50\}$$. Let $$\mathrm{A}=\{n \in s: n$$ is a square $$\}$$, $$\mathrm{B}=\{n \in s: n$$ is a prime$$\}$$ and $$\mathrm{C}=\{n \in s: n$$ is a square$$\}$$. Then, correct order of their probabilities is