Consider a fair coin with probability of heads and tails equal to $1 / 2$. Moreover consider two dice, first $\mathrm{D}_{1}$ that has three faces numbered $1,3,5$ and second $\mathrm{D}_{2}$ that has three faces numbered $2,4,6$. When rolled, for both $\mathrm{D}_{1}$ and $\mathrm{D}_{2}$, each of the three faces are equally likely.
A random experiment is conducted as follows. First, the coin is flipped once. If it shows heads, dice $\mathrm{D}_{1}$ is rolled once, while if the coin shows tails, $\mathrm{D}_{2}$ is rolled once, and the experiment ends.
Let $\mathrm{X}$ be the (random) number seen on the rolled dice in the experiment.
What is $\mathbb{E}[X]$ ?
- $\frac{7}{2}$
- $4$
- $3$
- $\frac{9}{2}$
- None of the above
