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.

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.
Hence, state the expected number of green cotton reels.

A company offers a $\$1000$ cash loan to anyone earning a monthly salary of at least $\$2000.$ To secure the loan, the borrower signs a contract with a promise to repay the $\$1000$ plus a fixed fee before $3$ months have elapsed. Failure to do this gives the company a legal right to take $\$1540$ from the borrower's next salary before returning any amount that has been repaid.

From past experience, the company predicts that $70\%$ of borrowers succeed in repaying the loan plus the fixed fee before $3$ months have elapsed.

Calculate the fixed fee that ensures the company an expected $40\%$ profit from each $\$1000$ loan.