A letter is expected to come either from city 'SURAT' or from city 'RAMPUR' through post office. If on the way, envelope containing the letter is damaged and only two consecutive alphabets RA are visible on it, then the probability that letter comes from the city 'SURAT' is :

The random variable X has a probability distribution P(X) of the following form, where k is some number.

$P(X=x) = \begin{cases} k, & \text{if } x=0 \\ 2k, & \text{if } x=1 \\ 3k, & \text{if } x=2 \\ 0, & \text{otherwise} \end{cases}$

Then $P(x \leq 2)$ is :

A random variable X has the following probability distribution:

Then, which of the following are correct ?

A. $k = 0.1$

B. $P(X<3) = 0.3$

C. $P(0<X<3) = 0.8$

D. $P(X>6) = 0.17$

Choose the correct answer from the options given below:

Let E and F are two independent events such that $P(E)=0.35$ and $P(E\cup F)=0.60$ then which of following statements are TRUE?

(A) $P(F)=\frac{5}{13}$

(B) $P(E|\overline{F})=0.35$

(C) $P(E|\overline{F})=0.65$

(D) $P(\overline{E}|\overline{F})=0.65$

Choose the correct answer from the options given below:

A pair of dice is thrown. If the two numbers appearing on them are different then the probability that the sum of the number is 6, is.

A die is thrown thrice. If the first throw is a four, then the chance of getting 11 as total sum, is

If A and B are two independent events such that $P(A) = \frac{4}{7}$ and $P(B) = \frac{2}{7}$ then $P(\overline{A} \cap \overline{B})$ equals