Pairwise Independence $\neq$ Mutual Independence

Probability Level 1

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.

Pairwise Independence ≠\neq​= Mutual Independence

Pairwise Independence $\neq$ Mutual Independence