$(2$ points$)$

Two events $E1$ and $E2$ are called independent if $p(E1E2)=p(E1)p(E2).$ For each of the following pairs of events, which are subsets of the set of all possible outcomes when a coin is tossed three times, determine whether or not they are independent.

a$)$ E$1$: tails comes up with the coin is tossed the first time; $E2$ : heads comes up when the coin is tossed the second time.

b$)$ E$1$: the first coin comes up tails; $E2$ : two, and not three, heads come up in a row.