The discrete random variable $V$ is such that $V\in \left\{1, 2, 3\right\}.$ Given that $P\left(V=1\right)=P\left(V=2\right)=2\times P\left(V=3\right),$ draw up the probability distribution table for $V.$

At a garden centre, there is a display of roses: $25$ are red, $20$ are white, $15$ are pink and $5$ are orange. Three roses are chosen at random. Show that the probability of selecting three red roses is approximately $0.0527.$

At a garden centre, there is a display of roses: $25$ are red, $20$ are white, $15$ are pink and $5$ are orange. Three roses are chosen at random.

Find the probability that at least one red rose is selected.

Three vehicles from a company's six trucks, five vans, three cars and one motorbike are randomly selected and tested for roadworthiness.

Draw up the probability distribution table for the number of vans selected.

A fair $4$ -sided die, numbered $1, 2, 3$ and $5,$ is rolled twice. The random variable $X$ is the sum of the two numbers on which the die comes to rest.

Show that $P\left(X=8\right)=\frac{1}{8}$

A fair $4$ -sided die, numbered $1, 2, 3$ and $5,$ is rolled twice. The random variable $X$ is the sum of the two numbers on which the die comes to rest.

Draw up the probability distribution table for $X$.

In a game, a player attempts to hit a target by throwing three darts. With each throw, a player has a $30\%$ chance of hitting the target.

Draw up the probability distribution table for $H,$ the number of times the target is hit in a game.

Two students are randomly selected from a class of $12$ girls and $18$ boys.

Calculate the variance of the number of girls selected.