Which of the following arguments are correct and which are not correct? Give reasons for your answer.
$(i)$ If two coins are tossed simultaneously,there are three possible outcomes - two heads,two tails,or one of each. Therefore,for each of these outcomes,the probability is $\frac{1}{3}$.
$(ii)$ If a die is thrown,there are two possible outcomes - an odd number or an even number. Therefore,the probability of getting an odd number is $\frac{1}{2}$.

(A) $(i)$ $Incorrect$
When two coins are tossed,the possible outcomes are $(H, H), (H, T), (T, H),$ and $(T, T)$.
It can be observed that there can be one of each in two possible ways: $(H, T)$ and $(T, H)$.
Therefore,the probability of getting two heads is $\frac{1}{4}$,the probability of getting two tails is $\frac{1}{4},$ and the probability of getting one of each is $\frac{2}{4} = \frac{1}{2}$.
Thus,the probability for each of these outcomes is not $\frac{1}{3}$.
$(ii)$ $Correct$
When a die is thrown,the possible outcomes are $1, 2, 3, 4, 5,$ and $6$. Out of these,$1, 3, 5$ are $odd$ and $2, 4, 6$ are $even$ numbers.
Since there are $3$ odd numbers out of $6$ total outcomes,the probability of getting an odd number is $\frac{3}{6} = \frac{1}{2}$.