Determine the probability $p$, for each of the following events.
(i) An odd number appears in a single toss of a fair die.
(ii) Atleast one head appears in two tosses of a fair coin.
(iii) A king, 9 of hearts or 3 of spades appears in drawing a single card from a well shuffled ordinary deck of 52 cards.
(iv) The sum of 6 appears in a single toss of a pair of fair dice.
(i) When a die is throw the possible outcomes are
$$\begin{aligned} S & =\{1,2,3,4,5,6\} \text { out of which } 1,3,5 \text { are odd, } \\ \therefore \text { Required probability } & =\frac{3}{6}=\frac{1}{2} \end{aligned}$$
(ii) When a fair coin is tossed two times the sample space is
$$S=\{H H, H T, T H, T T\}$$
In at least one head favourable enonts are $H H, H T, T H$
$\therefore$ Required probability $=\frac{3}{4}$
(iii) Total cards $=52$
$$\begin{aligned} \text { Favourable } & =4 \text { king }+2 \text { of heart }+3 \text { of spade }=4+1+1=6 \\ \therefore \quad \text { Required probability } & =\frac{6}{52}=\frac{3}{26} \end{aligned}$$
(iv) When a pair of dice is rolled total sample parts are 36 . Out of which $(1,5),(5,1),(2,4)$, $(4,2)$ and $(3,3)$.
$\therefore$ Required probability $=\frac{5}{36}$
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