a) What is the probability of obtaining 2 Heads when a coin is tossed twice?

Question

b) What is the probability of obtaining 1 Head when a coin is tossed twice?

Keep in mind, the coins are not tossed simultaneously.

Answer 1

Taking H = getting heads, and T = getting tails,

The sample space of the event of tossing a coin twice is as follows:

S = {(H,H),(T,H),(H,T),(H,H)}

There are a total of four outcomes.
Probability of an event = (Favourable outcomes/Total outcomes)

a) Fav. outcomes = 1
P(E) = 1/4

b) Fav. outcomes = 2
P(E) = 2/4 = 1/2

Answer 2

PS, your question made the point:
"Keep in mind, the coins are not tossed simultaneously."

The outcomes of two coins tossed simultaneously or a single coin tossed twice in succession would be the same.
The same would be true for 3 coins tossed simultaneously or a single coin tossed 3 times in succession,
4 coins ... , etc.