If E and F are two events such that P(E) = 0.8, P(F) = 0.7 and P(E ∩ F) = 0.6 then $P(\bar{E}/\bar{F})$ is:

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.

The probability distribution of a random variable X is given by

If k > 0, then $P(0 < X \leq 2)$ is equal to

A shopkeeper sells three types of flower seeds $A_1, A_2, A_3$. They are sold as a mixture where the proportions are 4 : 4 : 2 respectively. The germination rates of the three types of seeds are 45%, 60% and 35% respectively. Calculate the probability in the following cases.

The probability that seed will not germinate, given that the seed is of type $A_3$.

A random variable X has the following probability distribution:

The variance of X will be

A die is thrown three times. If the first throw is a five, the probability of getting 14 as the sum is

If A and B are independent events, then which of the following statements are TRUE?

(A) $P(A \cap B) = P(A).P(B)$

(B) $P(A \cap B) = P(A) - P(B)$

(C) $P(A \cup B) = P(A) + P(B) - P(A).P(B)$

(D) $P(A \cap B) = P(A). P(B|A)$

Choose the correct answer from the options given below: