12. Two unbiased coins are tossed. Calculate the probability of getting
a) Exactly two heads
b) At least two tails
c) At most two tails

When 2 unbiased coins are tossed together, then the sample space is given by
S = $\left\{ \mathrm{HH}, \mathrm{HT}, \mathrm{TH}, \mathrm{TT} \right\}$

Therefore n (S) = 4

F be the event of getting exactly 2 heads.
F = {HH}
n (F) = 1

G be the event of getting atleast 2 tails.
G = {TT}
n (G) = 1

Let E be the event of getting at-most 2 tails.
then, E =  event of getting 0 tail or 1 tail or 2 tail.
or E = $\left\{ \mathrm{TT}, \mathrm{HT}, \mathrm{TH}, \mathrm{HH} \right\}$
Therefore, n (E) = 4

Thus,
P (getting exactly 2 heads) = $\frac{n \left(\mathrm{F}\right)}{n \left(\mathrm{S}\right)} = \frac{1}{4}$

P (getting atleast 2 tails) = $\frac{n \left(\mathrm{G}\right)}{n \left(\mathrm{S}\right)} = \frac{1}{4}$

P (getting at-most 2 tails) = $\frac{n \left(\mathrm{E}\right)}{n \left(\mathrm{S}\right)} = \frac{4}{4} = 1$