Determine the probability \mathrm{p}, for each of the fonowing,
(a) An odd number appears in a single toss of a fair die.
(b) At least one head appears in two tosses of a fair coin.
Determine the probability \mathrm{p}, for each of the fonowing,
(a) An odd number appears in a single toss of a fair die.
(b) At least one head appears in two tosses of a fair coin.

Solution:
(a) When a fair die is thrown, the possible outcomes are
S=\{1,2,3,4,5,6\}
\therefore Total no. of outcomes =6 and the odd numbers are 1,3,5
\therefore Favourable no. of outcomes =3
We know that, Probability =\frac{\text { Number of favourable outcomes }}{\text { Total number of outcomes }}
\therefore Required probability =\frac{3}{6}=\frac{1}{2}

(b) When a fair coin is tossed two times, the sample space is
\mathrm{S}=\{\mathrm{HH}, \mathrm{HT}, \mathrm{TH}, \mathrm{TT}\}
\therefore Total no. of outcomes =4
Favourable cases are \mathrm{HH}, \mathrm{HT} and \mathrm{TH}.
\therefore Favourable no. of outcomes =3
It is known that,
\begin{array}{l} \text { Probability }=\frac{\text { Number of favourable outcomes }}{\text { Total number of outcomes }} \\ \therefore \text { Required probability }=\frac{3}{4} \end{array}