Step 1

(b) Given that the coin is fair

Therefore, the probability of head and tail for the coin is same which is 12.

The sample space for the a coin tossed is:

\[\begin{array}{|c|c|} \hline Outcome & head&tails \\ \hline Probability&\frac{1}{2}&\frac{1}{2} \\ \hline \end{array}\]

Determine the probability of whole sample space.

\(\displaystyle{P}={\frac{{{1}}}{{{2}}}}+{\frac{{{1}}}{{{2}}}}\)

\(\displaystyle={1}\)

Therefore, it is verified that the probability of whole sample space is 1.

Step 2

Determine the probability of head.

\(\displaystyle{p}={\frac{{\text{favourable outcome}}}{{\text{Total outcome}}}}\)

Substitute the respective values.

\(\displaystyle{p}={\frac{{{1}}}{{{2}}}}\)

Therefore, the probability of heads is \(\displaystyle{\frac{{{1}}}{{{2}}}}\).

(b) Given that the coin is fair

Therefore, the probability of head and tail for the coin is same which is 12.

The sample space for the a coin tossed is:

\[\begin{array}{|c|c|} \hline Outcome & head&tails \\ \hline Probability&\frac{1}{2}&\frac{1}{2} \\ \hline \end{array}\]

Determine the probability of whole sample space.

\(\displaystyle{P}={\frac{{{1}}}{{{2}}}}+{\frac{{{1}}}{{{2}}}}\)

\(\displaystyle={1}\)

Therefore, it is verified that the probability of whole sample space is 1.

Step 2

Determine the probability of head.

\(\displaystyle{p}={\frac{{\text{favourable outcome}}}{{\text{Total outcome}}}}\)

Substitute the respective values.

\(\displaystyle{p}={\frac{{{1}}}{{{2}}}}\)

Therefore, the probability of heads is \(\displaystyle{\frac{{{1}}}{{{2}}}}\).