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
A five-digits number is formed by using the digits $$1,2,3,4,5$$ with no repetition. The probability that the numbers 1 and 5 are always together, is