In a scratch-card game, the prize $V$ dollars from one card is a discrete random variable with $\text{P}(V=0)=0.25$, $\text{P}(V=5)=k+0.05$, $\text{P}(V=10)=2k$ and $\text{P}(V=25)=0.10$, where $k$ is a real constant.

Noah tosses three unbiased coins and spins a fair spinner with four equal sectors labelled $0$, $1$, $2$, and $3$. His score $Y$ is the number of tails shown plus the number on the spinner.

A bicycle hire station records the net change in the number of bicycles during a 30-minute period. A negative value means more bicycles were hired than returned. Let $N$ represent the net change in one period. The probability distribution for $N$ is shown below.

Assume different periods are independent.

Isla enters a badminton tournament where she plays three matches every day. The results of each match are independent of each other. Let $X$ be the number of matches Isla wins on any given day of the tournament. The probability distribution for $X$ can be modelled by the following table.

Rafi enters the same badminton tournament. Let $Y$ be the number of matches Rafi wins on any given day of the tournament. The probability distribution for $Y$ can be modelled by the following table.

On the final day of the tournament, both Isla and Rafi play their three respective matches and their results are independent. The number of matches Isla and Rafi win are then added together to form a total of six.