Pairwise Independence $\neq$ Mutual Independence

Let $X$ and $Y$ be random variables describing independent tosses of a fair coin. Let $Z$ be the random variable that equals $1$ if both $X$ and $Y$ land heads and that equals 0 otherwise.

How many of the following statements are true?

• The collection of random variables $\{X, Y\}$ is independent.
• The collection of random variables $\{X, Z\}$ is independent.
• The collection of random variables $\{Y, Z\}$ is independent.
• The collection of random variables $\{X, Y, Z\}$ is independent.