Three defective bulbs are mixed with $8$ good ones. If three bulbs are drawn one by one with replacement, the probabilities of getting exactly $1$ defective, more than $2$ defective, no defective and more than $1$ defective respectively are:

In a box containing 100 bulbs, 10 are defective. Then the probability, that out of a sample of 5 bulbs none is defective, is:

Match List-I with List-II

Let $A$ and $B$ be two events such that $P(A) = 0.2$, $P(B) = 0.4$, $P(B|A) = 0.5$

Choose the correct answer from the options given below:

If two cards are drawn at random without replacement from a pack of 52 playing cards, then the probability that both the cards are red, is

Which is the most suitable definition for random variable among the options given below:

Two dice are thrown simultaneously. If X denotes the number of sixes appearing on two dice, then which of the following are correct?

(A) $P(X=0)=\frac{1}{36}$

(B) $P(X=1)=\frac{10}{36}$

(C) $P(X=1)+P(X=0)=\frac{35}{36}$

(D) $P(X=1)+P(X=2)=\frac{11}{36}$

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.