A letter is known to have come either from LONDON or CLIFTON. On the envelop just two consecutive letter 'ON' are visible. The probability that the letter has come from LONDON is:

The probability that A hits a target is $\frac{1}{5}$ and the probability that B hits it is $\frac{2}{3}$. The probability that the target will be hit if both A and B shoot at it independently is:

The probability that exactly two of them complete the task on time is

Two persons A and B throw a die alternately till one of them gets a 'three' and wins the game. The probability of A's winning if A starts first is

If A and B are two events such that $P(A) = \dfrac{3}{10}, P(B) = \dfrac{2}{5}$ and $P(A \cup B) = \dfrac{3}{5}$, then $P(B|A) + P(A|B)$ is:

Which of the following statements are NOT correct about Standard Normal Distribution?

(A) The probability curve of the Standard Normal Distribution is a bell-shaped curve.

(B) The Standard Normal variate (Z) score describes the position of each data point in terms of its distance from the mean, when measured in standard deviation units.

(C) The Z-score is negative if the data point lies above the mean, and positive if it lies below the mean.

(D) There is a 95.45 % probability of randomly selecting a score between $\mu - \sigma$ and $\mu + \sigma$, when $\sigma$ is standard deviation and $\mu$ is mean.

Choose the correct answer from the options given below:

The random variable $x$ has a probability distribution $p(x)$ of the form $P(x=r)=\begin{cases} rk, & \text{if } r \le 2, \\ (r-1)k, & \text{if } 2<r\le 4, \\ 0, & \text{otherwise,} \end{cases}$ where $r \in \mathbb{N}\cup\{0\}$ and $k\in\mathbb{R}$, where $\mathbb{N}$ is the set of natural numbers. Then:

(A) $k=\frac{1}{9}$

(B) $P(2\le x\le 3)=\frac{1}{2}$

(C) $P(x=4)=\frac{1}{3}$

(D) $P(x>1)=\frac{7}{8}$

Choose the correct answer from the options given below.