Two ordinary fair dice are rolled. The discrete random variable $X$ is the lowest common multiple of the two numbers rolled.

Find $E\left(X\right)$ and $P\left[X\mathit{>}E\left(X\right)\right]$.

Two ordinary fair dice are rolled. The discrete random variable $X$ is the lowest common multiple of the two numbers rolled.

Calculate Var $\left(X\right).$

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.

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.

How many times is the target expected to be hit in $1000$ games?

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

Find the expected number of girls and the expected number of boys.

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

Write the ratio of the expected number of girls to the expected number of boys in simplified form. What do you notice about this ratio?

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

Calculate the variance of the number of girls selected.

A sewing basket contains eight reels of cotton: four are green, three are red and one is yellow. Three reels of cotton are randomly selected from the basket.

Show that the expected number of yellow cotton reels is $0.375.$

A sewing basket contains eight reels of cotton: four are green, three are red and one is yellow. Three reels of cotton are randomly selected from the basket.
Find the expected number of red cotton reels.