A coin is tossed twice. The following table shows the probability distribution of number of tails:
 

X	0	1	2
P(X)	K	6K	9K

(a) Find the value of K.
(b) Is the coin tossed biased or unbiased? Justify your answer.

(a) We know that, the Total probability should be equal to 1 for sum of all possible events under the given experiment.
Therefore,
$\begin{array}{l}\mathrm{P}\left(0\right)+\mathrm{P}\left(1\right)+\mathrm{P}\left(2\right)=1\\ \therefore \mathrm{K}+6\mathrm{K}+9\mathrm{K}=1\text{ (From the table) }\\ \therefore 16\mathrm{K}=1\\ \therefore \mathrm{K}=1/16\end{array}$
(b) From results we can see that events are not equally likely, hence the coin tossed is unbiased,
Because $\mathrm{P}\left(0\right)\ne \mathrm{P}\left(2\right)$
$\therefore \mathrm{K}\ne 9\mathrm{K}$
Therefore,
(a) The value of K = 1/16
(b) The coin tossed is unbiased because $\mathrm{P}\left(0\right)\ne \mathrm{P}\left(2\right)$