Kronecher product of a deterministic vector with a random vector

Question

Assume vector $a=[1,1,1,1,1]^T$ and vector $b_{5 \times 1}$ whose elements can be $0$ or $1$ with the probability $\frac{1}{2}$.

1) Is $a \otimes b$ a fully random vector?

2) The same question when we fix some elements of $b$ equal to $1$.